Richard S. Ellis

Ph.D., New York University, 1972 M.S., New York University, 1971 B.A., Harvard University, 1969 Mailing Address:     Department of Mathematics and Statistics     Lederle Graduate Research Tower, Box 34515     University of Massachusetts     Amherst, MA 01003-4515     USA Office: Room 1428, Lederle Graduate Research Tower Office Phone: 413-545-3125 Home Phone: 413-253-2492 Home Address: 763 Bay Road, Amherst MA 01002-3544 Fax: 413-545-1801 (work), 413-253-0172 (home) Email: rsellis_at_math_ dot_umass_dot_edu Additional Academic Appointment:     Adjunct Professor, Department of Judaic and Near Eastern Studies                                             University of Massachusetts at Amherst       See Section 7 for further information. Online copies of research papers and lecture notes in mathematics

Photograph by Ben Barnhart, computer graphics by Donna Meisse for UMass Magazine This photograph accompanies the article “Mediums of Vast Extent: A ‘Rare Intellectual Juggling Act.’” Click for an explanation of the photo. A photo in the garden of the Emily Dickinson Homestead appears in the photo gallery. It accompanies the article “The Poet and the Mathematician.” “As a rule, mathematicians do not write scholarly critiques of poetry and the Bible: the exception to the rule, Professor Richard Ellis.”

Some Highlights The Beginning of Wisdom.   Life as a miracle My Jewish-Buddhist Book.   Self-healing, meditation, and the Torah My 1985 Book.   Its Importance Book has been reprinted.   My 1985 book is reprinted in 2005 Award.   UMass Outstanding Faculty Award for Research Grant.   Grant from the National Science Foundation Paper.   Research article featured in Nonlinearity Translations.   Two articles on Torah translated into Polish Buddhist Teachings.   Meditation, emptiness, the four noble truths, . . . Indra’s Net.   Teachings and digital image Jewish Spirituality.   The path of blessing, emptiness, 1020 tovot, . . . Gliding.   Gliding into an interview for SIAM News Preserving Jewish Memory.   The Lithuania Project of my son Michael Convergence.   Buddhism, Judaism, poetry, prose Contents Section 0.   The Beginning of Wisdom: Life as a Miracle Section 1.   Research in Mathematics Section 2.   Online Copies of Research in Mathematics Section 3.   Other Mathematical Items Section 4.   Teaching Material in Mathematics Section 5.   My 1985 Book Is Reprinted in 2005 Section 6.   My Jewish-Buddhist Book: Self-Healing and Spirituality Section 7.   Judaic Studies and Literature Section 8.   Translation into Polish of Two Articles on Torah Section 9.   Activities in Jewish Affairs Section 10.   Additional Writings Section 11a.   Buddhist Spirituality Section 11b.   Jewish Spirituality Section 12.     Honors and Awards Section 13.     Newspaper and Magazine Articles About My Work Section 14.     Biographical Profiles Section 15.     Preserving Jewish Memory in Lithuania Section 16.     Convergence: Buddhism, Judaism, Poetry, Prose

Photograph by Carol Lollis for Amherst Bulletin Both Kafka and I love this photograph taken in our book-lined cave. Click to see an enlarged version. The photo accompanies the article “Expecting the Unexpected: Deviations Common in Life of Math Professor.” Chancellor John V. Lombardi presenting me with the Outstanding Faculty Award for Research in the College of Natural Sciences and Mathematics, University of Massachusetts at Amherst. Click to see an enlarged version.

Overwhelmed with inexorable, intoxicating gratitude.   Before he began, Alessandro leaned back in his chair and looked at the sky as if to take refreshment from the light. “When I came back from the war I had lost everything, but I was grateful nonetheless to be alive. Despite what I had seen, despite the destruction of all I had once taken for granted, despite the wounds I had sustained and my memory of men, far better than me, who were obliterated, I was overwhelmed with gratitude, inexorable, intoxicating gratitude.”
      Mark Helprin, A Soldier of the Great War, page 743

0. The Beginning of Wisdom: Life as a Miracle

The Wonder of It All
by Ralph Marston

Do you ever wonder
At the wonder of it all?

Do you ever stand in awe
of the tiniest things
and how perfectly they work together?

Do you ever stop to think
about all the possibilities
and how even though they have no limit
they grow in number with every minute?
. . .

Dawn After the Hurricane
Photograph by Bob Schwartz

1. Research in Mathematics

When Lawrence understood, it was as if the math teacher had suddenly played the good part of Bach’s Fantasia and Fugue in G Minor on a pipe organ the size of the Spiral Nebula in Andromeda — the part where Uncle Johann dissects the architecture of the Universe in one merciless descending ever-mutating chord, as if his foot is thrusting through skidding layers of garbage until it finally strikes bedrock.
      Neal Stephenson, Cryptonomicon, page 7

This is the kind of question Henry liked to put to himself when he was a schoolboy: what are the chances of this particular fish, from that shoal, off that continental shelf ending up in the pages, no, on this page of this copy of the Daily Mirror? Something just short of infinity to one. Similarly, the grains of sand on a beach, arranged just so. The random ordering of the world, the unimaginable odds against any particular condition, still please him. Even as a child, and especially after Aberfan, he never believed in fate or providence, or the future being made by someone in the sky. Instead, at every instant, a trillion trillion futures; the pickiness of pure chance and physical laws seemed like freedom from the scheming of a gloomy god.
      Ian McEwan, Saturday, pages 128–129

1. Current Research.   My current research focuses on the theory of large deviations with applications to statistical mechanics.
   
   
2. Equivalence and Nonequivalence of Ensembles.   My current research on applications of probability theory to statistical mechanics focuses on a problem that is fundamental to the entire subject. Which of the two basic probability distributions — the microcanonical ensemble or the canonical ensemble — is the appropriate choice for calculating equilibrium properties of statistical mechanical systems? Although it is widely assumed that the two ensembles give equivalent results in the thermodynamic limit or the continuum limit, my recent research shows that for general systems this is not the case. In fact, from the viewpoint of equilibrium macrostates, the microcanonical ensemble is in general richer and more basic than the canonical ensemble (see items (2) – (5) in the next paragraph). The basic theoretical results are derived in the paper “Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles,” written with Kyle Haven and Bruce Turkington. The results have been applied to a model of geophysical fluid turbulence and to two spin systems, the mean-field Blume-Emery-Griffiths model and the Curie-Weiss-Potts model.
   
   
   
3. Beautiful Connections: Equivalence and Nonequivalence of Ensembles, Solutions of Two Minimization Problems, and Concavity Properties of the Microcanonical Entropy.   A basic problem in the asymptotic analysis of the microcanonical and canonical ensembles is to understand the relationship between the sets E(u) and E(β) of microcanonical and canonical equilibrium macrostates; u and β denote fixed values of the mean energy and the inverse temperature. As we prove in our paper “Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles,” the relationships between these sets are determined by concavity properties of the microcanonical entropy s(u). Here is a quick summary of the results in that paper. Click to read a leisurely overview of these results together with an application to spin systems.
           (1) Minimization problems. The elements of E(u) solve a constrained minimization problem, and the elements of E(β) solve a dual unconstrained minimization problem.
           (2) Canonical is always microcanonical. For fixed β each element of E(β) belongs to E(u) for some u.
           (3) Full equivalence. E(u) equals E(β) for some β if and only if s is strictly concave at u.
           (4) Partial equivalence. E(u) is a proper subset of E(β) for some β if and only if s is concave at u but not strictly concave.
           (5) Nonequivalence. E(u) is disjoint from E(β) for all β if and only if s is not concave at u.
   Because of items (2) – (5), we conclude that in general the microcanonical ensemble is richer and more basic than the canonical ensemble. The following are recommended.
   
   • Our paper on the mean-field Blume-Emery-Griffiths spin model exhibits the relationships between concavity properties of the microcanonical entropy and ensemble equivalence via graphs.
   • Our paper on the Curie-Weiss-Potts spin model, which is the Potts model on the complete graph on n vertices, studies analytically the relationships between concavity properties of the microcanonical entropy and equivalence of ensembles.
   • Our paper on a model of geophysical fluid turbulence highlights an overview of the theory, graphical results, and a theorem on the nonlinear stability of the steady mean flows corresponding to microcanonical equilibria.
   • An exposition of our theory of ensemble equivalence with an emphasis on the underlying physical principles is given in Hugo Touchette’s Ph.D. dissertation and in our paper “An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles.”
   
   
4. The Generalized Canonical Ensemble and Universal Ensemble Equivalence.   If the microcanonical ensemble is not equivalent with the canonical ensemble, then is it possible to replace the canonical ensemble with a generalized canonical ensemble that is fully equivalent with the microcanonial ensemble? This motivational question inspired our paper “The Generalized Canonical Ensemble and Its Universal Equivalence with the Microcanonical Ensemble.” The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function g of the Hamiltonian. The main result in our paper is that the microcanonical and generalized canonical ensembles satisfy the same relationships as the microcanonical and standard canonical ensemble given in items (1)–(5) in the preceding paragraph with the microcanonical entropy s replaced by the generalized microcanonical entropy s–g . The considerable freedom that one has in choosing g has the important consequence that even when the microcanonical and standard canonical ensembles are not equivalent, one can often find g with the property that the microcanonical and generalized canonical ensembles satisfy a strong form of equivalence that we call universal equivalence. For example, if the microcanonical entropy is C², then universal equivalence of ensembles holds with g taken from a class of quadratic functions. This use of functions g to obtain ensemble equivalence is a counterpart to the use of penalty functions and augmented Lagrangians in global optimization. An overview of the results in our paper is available online in a talk that I gave at the Technische Universität Berlin.
   
   
5. Statistical Mechanical Theories of Turbulence.   Other recent research has focused on statistical mechanical theories of turbulence. A distinguishing feature of turbulence phenomena is that coherent structures are formed on large scales while random fluctuations are generated on small scales. A major goal of any statistical mechanical theory is to give a mathematical characterization of coherent structures and to predict their formation, interaction, and stability. Coherent structures are observed on all scales in nature. Examples are vortices and shears in fluid motion; the Great Red Spot of Jupiter, a hurricane-like storm system at least twice the diameter of Earth; Earth ocean waves such as tsunamis and waves on a beach; charge density waves in certain solid state materials; pulses in optical fibers; solitons; and smoke rings.
   
   
   Cassini at Jupiter: Red Spot Movie
   Credit: CICLOPS, NASA, JPL, University of Arizona
   
6. Successes.   My coworkers and I have developed a body of mathematical techniques — based on the theory of large deviations and other methods — that settle many of the key questions arising in the statistical equilibrium theory of 2D fluid turbulence (governed by the 2D Euler equation), geostrophic turbulence (governed by the quasi-geostrophic potential vorticity equation), dispersive wave turbulence (governed by a class of nonlinear Schrödinger equations), and related areas. Future research will focus on nonequilibrium phenomena. A stunning application of our equilibrium techniques is the work of B. Turkington, A. Majda, K. Haven, and M. DiBattista (Proc. Nat. Acad. Sci. USA, 98:12346–12350, 2001) on predicting the jetstreams and vortices in the Jovian atmosphere, the best known example of which is the Great Red Spot. Their paper is the first work in which the sophisticated statistical theories developed by myself and coworkers are synthesized with actual observational data from the Voyager and Galileo space missions.
   
   
7. The National Science Foundation is funding my research project with Bruce Turkington during the period July 1, 2006 – June 20, 2009. Entitled “Equilibrium and Nonequilibrium Statistical Mechanics Applied to Reduced Descriptions of Complex Systems,” the interdisciplinary project addresses cross-cutting topics in analysis, modeling, and computation of stochastic systems.
   
   
8. Lecture Notes and Survey Papers on Large Deviations and Applications.   The following lecture notes and papers of mine survey basic results in the theory of large deviations and then apply the theory to several problems in statistical mechanics.
   • “The Theory of Large Deviations and Applications to Statistical Mechanics.” Lectures for the International Seminar on Extreme Events in Complex Dynamics, October 23–27, 2006 (115 pages). Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany.
   • “The Theory of Large Deviations: From Boltzmann’s 1877 Calculation to Equilibrium Macrostates in 2D Turbulence,” Physica D, Volume 133, Numbers 1–4, 106–136 (1999).
   • “An Overview of the Theory of Large Deviations and Applications to Statistical Mechanics,” Scandinavian Actuarial Journal, Number 1, pages 97–142 (1995).
     
     
9. My 1997 Book Cowritten with Paul Dupuis.   Prior to my work on statistical theories of turbulence, I worked on large deviations for Markov processes with discontinuous statistics and applications to queueing theory. My 1997 book, cowritten with Paul Dupuis and entitled A Weak Convergence Approach to the Theory of Large Deviations, presents a new approach to large deviations that is well suited for such processes. The main theoretical contribution of the book is to show how one can replace the exponential estimates of standard large deviation approaches by law-of-large-numbers-type estimates, which are obtained by the theory of weak convergence. The book was published by John Wiley & Sons, from whom the book can be purchased online. A link to an online, pre-publication copy of our book in pdf-format is available. This online copy has no index and differs slightly from the published book.
           Along with coworkers I have applied the techniques of the book to study large deviation phenomena for small-noise diffusions with discontinuous drift, a random walk model with state-dependent noise that arises in the study of recursive algorithms, and a general class of queueing systems.
           Three reviews of my book are available online.
   
   • James Lynch:   “This is a very thoughtfully written book intended for theoretical statisticians who want to learn more about the theory as well as for experts of the theory.   . . .   I found A Weak Convergence Approach to the Theorv of Large Deviations to be an excellent book with a unique perspective on one of the most active areas in probability theory today. Its self-contained development facilitates reading (and makes it appropriate for more mathematically oriented graduate students), and its control theory perspective is appealing from a research standpoint. This book is well worth reading if one has any interest in this theory.”
   • A. Rukhin:   “[T]his new book gives a fresh perspective on the field by relating it to the classical theory of weak convergence.   . . .   Summing up, the material presented here is rich, and the method of weak convergence turns out to be unifying for a wide range of important problems of probability theory.”
   • M. Schweizer:   “This book presents a novel approach to the theory of large deviations by using ideas and results from control theory and weak convergence.   . . .   On the whole, this is an interesting and promising new approach to proving large deviation results. The book is rather technical (a total of five appendices covering almost 100 pages bear witness to this), but written and presented in a very careful manner, and comments between the results help to understand the key ideas.”
   
   
   
   
10. The Importance of My 1985 Book and the Gärtner-Ellis Theorem.   My 1985 book, entitled Entropy, Large Deviations, and Statistical Mechanics and published by Springer-Verlag, is now a standard reference in the field. In the words of one author, the book is “the definitive and now classic reference on large deviations and statistical mechanics.” Hugo Touchette discusses the importance of my 1985 book in the introduction to his review article, “The Large Deviation Approach to Statistical Mechanics.”

    “These points have already been recognized and ‘publicized’ to some extent by a number of people, who see large deviation theory as the proper mathematical framework in which problems of statistical mechanics can be formulated and solved efficiently and, if need be, rigorously. Ellis [90] is to be credited for providing what is perhaps the most complete expression of this view, in a book that has played a major part in bringing large deviations into physics.”

    The book features a large deviation theorem first proved by J. Gärtner and then generalized by me in the paper “Large Deviations for a General Class of Random Vectors,” Annals of Probability, 12:1–12 (1984). Now known as the Gärtner-Ellis theorem, it has been applied numerous times in the mathematical, statistical, physical, and engineering literature. For a comprehensive treatment of the theory of large deviations featuring applications and further generalizations, I recommend the monograph by A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, Second Edition, New York: Springer-Verlag, 1998. J. Gärtner's contribution to the Gärtner-Ellis Theorem and my contribution are discussed on page 68 of this monograph.
    
    Six reviews of my book are available online.
    
    • O. E. Barndorff-Nielsen:   “It is a strength of the book that the author, rather than aiming to give a very comprehensive account of the extensive subject areas he addresses, has chosen to focus on a limited number of judiciously chosen topics.   . . .   There are interesting connections to the theory of exponential families and to saddle-point approximations and in this relation the exposition of Varadhan’s extension of Laplace’s method deserves special mention. The book fills a lacuna in the literature in a splendid fashion.”
    • Peter Donnelly:   “In conclusion, it should be said that this book is really two books, an introduction to the theory of large deviations and an introduction to equilibrium statistical mechanics — two different areas, each with its own beauty and its own flavor, but, as the author hopes, each enriched by the other. The book is, quite simply, enjoyable, stimulating, and rewarding.   . . . [I]t presents a wonderful opportunity to learn about and gain insight into either field or both. For those who are at all interested, it is an opportunity that should not be lightly missed.”
    • Theodor Eisele:   “For the first time, the author systematically applies these three kinds of entropy functionals to the fundamental models of statistical mechanics.   . . .   The book is well organized and precisely written. It contains many notes, historical remarks, problems and suggestions for further reading. The list of references is extensive. It would be very well suited as a course book for an introduction to the mathematical methods of statistical mechanics.”
    • Peter Ney:   “It is clear that a great deal of thought and painstaking care has gone into the writing of this book. It is an important and very useful contribution to the literature on probability limit theory.”
    • S. Pigosian:   “Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completely self-contained reading and is written in a rather detailed manner.”
    • D. W. Stroock:   “Besides the fact that the author’s treatment of large deviations is a nice contribution to the literature on the subject, his book has the virtue that it provides a beautifully unified and mathematically appealing account of certain aspects of statistical mechanics. In particular, he carries out the program suggested by O. E. Lanford, III and substantiates, once again, that good mathematics often originates from good physics. Furthermore, he does not make the mistake of assuming that his mathematical audience will be familiar with the physics and has done an admirable job of explaining the necessary physical background. Finally, it is clear that the author’s book is the product of many painstaking hours of work; and the reviewer is confident that its readers will benefit from his efforts.”
    
    
11. Importance of My Work with Mark Pinsky on the Linearized Boltzmann Equation.   In the mid-1970’s Mark Pinsky of Northwestern University and I collaborated on a project involving the linearized Boltzmann equation, the first extensive project of my career. In June 2003 Mark informed me about the important role that our joint work has played in the further progress of the subject; in particular, in the study of viscous conservation laws. The attached email from Mark contains the text of an email from Jeffrey Humpherys, who describes recent applications of our ideas and then writes the following: “I can go on and on, but I wanted you to know that your work with Ellis is very important.” Our work on this project resulted in three papers, two written jointly and one written by Mark alone. These companion papers derive limit theorems and asymptotics that relate the linearized Boltzmann equation with the linear Euler and Navier-Stokes equations.
    • Richard S. Ellis and Mark Pinsky, “The First and Second Fluid Approximations to the Linearized Boltzmann Equation,” Journal de Mathématiques Pures et Appliquées 54:125–156 (1975).
    • Richard S. Ellis and Mark Pinsky, “The Projection of the Navier-Stokes Equations upon the Euler Equations,” Journal de Mathématiques Pures et Appliquées 54:157–182 (1975).
    • Mark Pinsky, “On the Navier-Stokes Approximation to the Linearized Boltzmann Equation,” Journal de Mathématiques Pures et Appliquées 55:217–231 (1976).

Coming Home
The Heron Weekly #18

2. Online Copies of Research in Mathematics

• Links are available to online copies of all my publications, all recent preprints, and some lecture notes in pdf-format.
  
  
• Online copies of selected talks in pdf-format are available.
  
  
• In 1997 John Wiley & Sons published the book A Weak Convergence Approach to the Theory of Large Deviations, which I cowrote with Paul Dupuis. A link to an online, pre-publication copy of our book in pdf-format is available. This online copy has no index and differs slightly from the published book.

Night Paddle
The Heron Weekly #41

3. Other Mathematical Items

1. Featured Article in Nonlinearity. My article, “Nonequivalent Statistical Equilibrium Ensembles and Refined Stability Theorems for Most Probable Flows,” written with Kyle Haven and Bruce Turkington, was published in Nonlinearity 15:239-255 (2002). On February 27, 2002, we were informed that this “article has been selected for inclusion on the as a Featured Article. . . . Featured Articles are chosen by the journal for their high quality and interest to readers.”
   
   
2. Publication List. Click to see an annotated list of selected publications and my complete publication list.
   
   
3. Curriculum Vitae. Click to see my complete curriculum vitae in mathematics and highlights of my curriculum vitae in mathematics, Judaic studies, and literature.
   
   
4. Ph.D. Dissertations. Click to see a list of Ph.D. dissertations that I have directed.
   
   
5. Comments by Students on Our Interactions.
   • Colin Shaw. A 2001 e-letter of appreciation from Colin A. Shaw, a former undergraduate student at the University of Massachusetts, can be viewed here.
     
     
   • Zoi Rapti. A 2003 e-letter of appreciation from Zoi Rapti, a former graduate student in my department, can be viewed here.
     
     
   • Scott Croshier. A 2003 e-letter of appreciation from Scott Croshier, a former undergraduate student at the University of Massachusetts, can be viewed here.
     
     
   • Sri Harsha Tharkabhushanam. A 2004 e-letter of appreciation from Sri Harsha Tharkabhushanam, a former graduate student in my department, can be viewed here.
     
     
   • Two Graduate Students. During the fall semester of 2004 I taught Math 623, a first-year graduate course on the general theory of measure and integration. In their anonymous evaluations two students wrote the following about my teaching.

     Student #1. Prof. Ellis did an absolutely amazing job teaching this course. Not only is it difficult to make people understand these new topics, but to come in every day prepared and give perfect lectures is a difficult task. He did both of these things to perfection. For the first time a professor made analysis interesting to me. He always found the best ways to explain hard topics in detail. He was excellent at not only motivating ideas, but excellent at giving step-by-step methods to get ideas through to his students. He was always helpful in office hours and very approachable. He took this class very seriously, and for that I am grateful. I look forward to being able to take another class with him some day. He did an excellent job.
     
     Student #2. Dr. Ellis is an absolutely wonderful teacher. He is an excellent communicator, and he has a wonderful classroom presence. He is thorough, without beating things into the ground, and works at a great pace. He has reasonable demands, and they are always tempered with compassion and understanding. I was really very nervous about the material, having not had analysis as an undergraduate (beyond calculus and sequences and series), and he really put the material out there at an accessible level. I think he is great.

   • Marius Costeniuc. Marius Costeniuc, a graduate student in my department, worked on his Ph.D. dissertation under my direction and will receive his degree in September 2005. In the first paragraph of the acknowledgements in his Ph.D. dissertation, he comments on our interaction.

     I would like to begin by thanking my advisor Richard S. Ellis, to whom I owe a deep debt of gratitude for his superb guidance, understanding, invaluable help, and great generosity and for teaching me not only about mathematics, but also about life. I would also like to thank him for his infinite kindness, for all his good advice inside and outside mathematics, and for doing so many nice things for me. Thank you for being so wonderful!

Through a serendipitous large deviation, the next artwork
led to my being interviewed for an article in SIAM News.


Gliding
The Heron Weekly #21

4. Teaching Material in Mathematics

• Teaching material for Math 331 (Fall 2006) is available here.
  
  
• Teaching material for Stat 515H (Fall 2006) is available here.

Flight Shadow
The Heron Weekly #26

5. My 1985 Book Is Reprinted in 2005. Will This End a Crime Wave in Paris?

On June 15, 2005 I was informed by Dr. Catriona M. Byrne that my 1985 book, entitled Entropy, Large Deviations, and Statistical Mechanics, would be republished by Springer-Verlag within the Classics in Mathematics series. Dr. Byrne is the Executive Director for Mathematics in Heidelberg, Germany. Here is a quotation from her letter.

“Your book Entropy, Large Deviations, and Statistical Mechanics (Grundlehren der Mathematischen Wissenschaften, Vol. 271), has been unavailable for some time. We are well aware of the significance of this book in the mathematical literature, even today, many years after its original publication, and would like to reprint it. . . . However, your book unquestionably belongs to the ‘modern classics’ of the field, and we know that there is a sizeable audience, in particular among the younger generation of mathematicians and mathematics students, who know of books like yours by reputation and would like to acquire them if they were available in a different price category.”

        Springer-Verlag began publishing books in higher mathematics in 1920, when the series Grundlehren der mathematischen Wissenschaften, initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later a new series Ergebnisse der Mathematik und ihrer Grenzgebiete, survey reports of recent mathematical research, was added.
        Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers.

An interesting story related to the reprinting of my book unfolded with an email sent to me in August 2003 by Emily Tanimura in Paris concerning the book, which was then out of print. Emily wanted to purchase the book is now out of print, but was having difficulty locating a copy to buy. In her next email she made the following startling revelation concerning a crime wave that my out-of-print book had caused.

“Perhaps it is time for Springer to print more copies. There seems to be a great demand. In Paris the book has become something of a collector’s item. Indeed my previous copy was stolen and so were the copies of most of our university libraries.”

Emily then suggested that this larceny should persuade Springer to reprint the book.

“[I]t is probably rare to have written a book that has caused a crime wave in the academic community. Against this background perhaps Springer could be persuaded that reprinting the book is a civic duty.”

Emily’s experience with my book involved multiple losses. First her own copy was stolen. Then all the libraries from which she tried to borrow a copy reported that the book had been stolen. Finally, a copy that she had borrowed from someone else was stolen. However, Emily transcended the negativity of her predicament by writing a witty and insightful account of her experiences. I am grateful to her for contributing to my web page her honest, humorous analysis of the corruptibility of the human soul.

Another way of regarding Emily’s experiences is suggested by a review of a poetry book written by a person whose copy of the book had been stolen from a pub. The reviewer wrote the following. “I took it to a pub, had a beer or two too many, left without the book. Realised it was left two minutes later, went back, too late! Gone. I figure whoever nabbed it was also in need of the clarity, the crystal limning, the in-your-face reality.” Could the same be said of any of the people who nabbed Emily’s copies of Entropy, Large Deviations, and Statistical Mechanics and who stripped this book from the mathematical libraries of Paris?

Is my book unique in this respect? When I communicated Emily’s experiences to a representative of Springer-Verlag, I received the following reply.

“What you write about its disappearing from various mathematical libraries is interesting. Similar things have been reported rather often of other books on stochastic processes, diffusions, large deviations, stochastic calculus, optimal stopping, and so on, ever since the great surge of interest in mathematical finance of recent years.”

Self-Help-Self-Healing
Theater of Life: “the Mind is the Builder”

6. My Jewish-Buddhist Book: Self-Healing and Jewish-Buddhist Spirituality

Starting in February 2000, debilitating headaches changed my life. I suffered from the pain and even more from my anger over the pain. How the headaches eventually became my greatest teacher is the subject of my book, which has the working title The Truth in My Face: How Buddhist Meditation Woke Me Up. I am now actively seeking a publisher.

The book tells the inspirational story of how Buddhist meditation woke me up and healed me after years of suffering from chronic headaches. Through meditation I was able to transform the suffering into an all-encompassing approach to my life. My goal in writing the book is to help other people become aware of the suffering in their lives and to help them heal that suffering. Buddhist teachings have also enabled me to view important aspects of my life differently, including mathematics and the Torah. In the book I offer innovative readings of several Torah narratives that will be spiritually nourishing to many readers who may be familiar with these narratives in a traditional way.

The following material is available online: chapter summaries, front matter, and introduction.

Great Egret Blue
The Heron Weekly #22

7. Judaic Studies and Literature

1. Adjunct Professor of Judaic Studies. Besides my regular academic appointment in the Department of Mathematics and Statistics at UMass, since 1998 I have been an Adjunct Professor in the Department of Judaic and Near Eastern Studies at UMass.
   
   
2. Publication List. Click to see my publication list with online copies of publications. These publications include essays on the Torah, the poetry of Emily Dickinson, Jewish-Christian relations, and the art of Michelangelo. Except for two essays that appeared in Conservative Judaism (see the next item), the online copies of my other publications are prepublication versions that do not necessarily coincide with the published versions of the essays. My essay on Jewish-Christian relations, entitled “A Jew in Rome: Christian Antisemitism and the Holocaust,” was published in Midstream in two parts. In January 2006 I received an email from a person in Argentina who identified himself as Christian and who had read the essay online, finding it extremely moving. In my response I wrote the following.

   “Those experiences seem so long ago. I have not thought much about the topics of that essay since publication five and a half years ago. In fact, my obsession with Christian anti-Semitism, Nazis, and the Holocaust, which started in my youth and energized those essays as well as a novel I was not able to publish, seems to have passed. They were part of an earlier phase of my life.”

   Here is a quotation from the person's reply.

   “You are a gifted writer. Please don't give up with your unpublished novel, or keep the pen going in some other similar project. Something happened deep inside when I read the essay. You are handling powerful stuff when you write!”

3. Two Essays Published in Conservative Judaism. Publication versions of two essays that appeared in Conservative Judaism are available online. These essays are “The Book of Leviticus and the Fractal Geometry of Torah” and “Human Logic, God’s Logic, and the Akedah.” The online version of the essay, but not the published version, contains four images of the Mandelbrot set, each one based on a magnification of an area of the previous image. The Mandelbrot set is one of the best known examples of a fractal, which is a geometric object that displays self-similarity at multiple scales. The essay, “The Book of Leviticus and the Fractal Geometry of Torah,” appeared in the bibliography of the website Sacred Geometry Discovery — “Sacred Geometry is an art of memory which employs geometric forms as symbols, for the memory and organization of . . . divine wisdom.” — and was the vehicle that brought Willi Niemann and me together.
   
   
4. Curriculum Vitae. Click to see highlights of my curriculum vitae in mathematics, Judaic studies, and literature.
   
   
5. Annual Faculty Reports. Comments concerning my activities in Judaic Studies appear in two annual faculty reports. These comments can be viewed here.
   
   
6. My Novel, Blessings from the Dead. I have written a novel entitled Blessings from the Dead, which I have not been able to publish. The novel depicts the quest of a Jewish-American scientist for the truth about his mother, a woman he never knew. Rich in Jewish history and the Bible, the novel deals with the Holocaust, the Arab-Israeli conflict in modern-day Jerusalem, and the psychological effects of scientific creativity. A synopsis of the novel and the first chapter of the novel are available.
   
   
7. Courses That I Have Taught. Click to see a list of courses that I have taught at the Jewish Community of Amherst, the University of Massachusetts, and the Springfield Jewish Community Center.
   
   
8. Florence Melton Adult Mini-School. During the academic years 2001–2002, 2002–2003, and 2003–2004, I taught a course at the Springfield Jewish Community Center on Jewish texts. Entitled “The Purposes of Jewish Living,” the course is part of the Florence Melton Adult Mini-School. The Mini-School is an international network of more than 60 community-based schools offering adults the opportunity to acquire Jewish literacy in an open, trans-denominational, intellectually stimulating learning environment. More than 260 faculty and 6000 students are involved in the program.
           When in April 2004 I announced my decision to stop teaching in the Mini-School, the director of the program, Rabbi Jonathan Perlman, wrote the following in an email:

           “. . . I am sorry you will be leaving us. You have made a great impression on a lot of our students, and they will remember you fondly.”

           The 2002–2003 brochure for the Mini-School can be viewed here. Click to see the front side and the reverse side. A photo of me and a student appears in the upper right on the reverse side. In order to read the brochure, choose a larger text size in the browser and click on the icon that appears in the lower right corner of the screen.
   
   
9. Poetry from My Youth. Poetry from my youth can be viewed here.
   
   
10. Recent Poems. Three recent poems can be viewed here: “Moebius Strip” explores the relationships between a man, his son, and his dead father; “Breath” is a meditation on meditation; “Brewed in an Abbey Near Antwerp” is based on true events.

An image from the Mandelbrot set

8. Translation into Polish of Two Articles on Torah

The extraordinary sequence of events that began with an email from Dr. Willi Niemann shows why I maintain a web page. Willi is a physician and mathematician working in the fields of cancer and fractals in Poznan, Poland. In an email dated April 2, 2002, Willi asked me for permission to translate two of my articles into Polish and to post the translations on the web page of Bracia Polscy; in English Polish Brethren Unity. These articles are “The Book of Leviticus and the Fractal Geometry of Torah,” published in Conservative Judaism, and “Torah Talk: Terumah,” published in the Jewish Weekly News. In May 2003 my son and I visited Willi in Poznan, where I gave a talk at a Holocaust museum and two talks on the Torah.

Polish Brethren Unity, a Protestant Unitarian congregation, believes that “the Jews are a chosen people to be a light to the nations”; that “to understand Jesus’s teachings, one must understand first the messianic tradition of ancient Israel including Judaism in its beauty and depth”; that “only those who can approach the secret of Torah and its internal beauty have a chance to find the Presence of G-d, . . . to identify Jews as brothers and friends, and to appreciate their influence upon . . . Polish culture.” Willi felt that my articles would help facilitate a Polish-Jewish dialogue and would help reveal, at least in small measure, something of the “beauty of Hebrew theology and philosophy.” Concerning the contributions of Jews to Polish culture, he wrote that “we consider . . . Jews as our brothers in messianic hope and friends . . . [and] all Polish Jews as our fellows. . . . Polish culture flourished when you dwelled with us . . . [and] lost much you disappeared suddenly from our public life.”

When I asked Willi how he discovered my writings on the internet, he wrote the following.

“From time to time, I search Internet for scientific articles. As you may know, I am interested in fractal analysis. All of a sudden, I found your name associated with your article on fractals and Thora. That was very intriguing. I printed it out, read, and came to conclusion that the text is very spiritual, delicate, and expresses something more than just simple explanation of some biblical terms and ideas. I decided to write to you and ask for permission to translate it into Polish because there are very [few] biblical pages in Polish. And I thought that some people might enjoy reading about Thora in that way. Then I found the other articles of yours, visited your www page, found that our scientific interests have much in common.”

• Click here to see highlights of my email correspondence with Dr. Willi Niemann. This correspondence contains the following material: (1) history of Polish Brethren Unity, (2) their doctrinal beliefs, (3) their desire to change Polish views of Jews, (4) comments on Jewish-Christian dialogue in Poland.
  
  
• The Polish translation of “The Book of Leviticus and the Fractal Geometry of Torah” can be viewed here. This d’var Torah on Be-har (Leviticus 25:1-26:2) elucidates the symbiotic relationship between the laws of Leviticus and the narratives of Genesis and Exodus.
  
  
• The Polish translation of “Torah Talk: Terumah” can be viewed here. This d’var Torah on Terumah (Exodus 25:1-27:19), published in the Jewish Weekly News, January 26, 1995, page 12, is a meditation on how our lives and the symbols of this parashah are intertwined.

Loon Lake Arising
The Heron Weekly #51

9. Activities in Jewish Affairs

• From April 1994 to February 1998 I was a co-chair of the Jewish Faculty and Staff Group at the University of Massachusetts Amherst. I worked with three other co-chairs: David Bloome, Maurianne Adams, and Marilyn Kushick. The Jewish Faculty and Staff Group worked closely with Rabbi Saul Perlmutter, Executive Director of UMass Hillel, in addressing issues of Jewish identity and concern. These issues included deciding upon and implementing effective actions to protest anti-Semitic speakers on campus.
  
  
• As co-chair of the Jewish Faculty and Staff Group, I helped organize a Torah study group and applied for National Hillel Faculty grants from the Jacob Burns Endowment in Ethics to support faculty programs. These grants supported the following three mini-conferences:
  1. “Balancing Our Roles as Jewish Faculty and Staff at UMass" on December 3, 1995 (with co-chair Maurianne Adams),
  2. “Ways of Coming Together: Being Jewish in America” on November 24, 1996 (with co-chair Marilyn Kushick),
  3. “Jewish Identity and the Arts: Our Work and Our Heritage” on November 16, 1997 (with co-chair Marilyn Kushick).
  
  
  
• On May 2, 1995, an anti-Semitic letter was published in the Massachusetts Daily Collegian, the student newspaper at the University of Massachusetts Amherst. The response to this anti-Semitic letter by the Jewish Faculty and Staff Group can be viewed here. The letter was written by David Bloome and myself, who were the co-chairs of the Jewish Faculty and Staff Group at the time.
  
  
• During the academic years 1993-1994 and 1994-1995, I was a member of the Chancellor’s Task Force on Jewish Awareness and Anti-Semitism, the purpose of which was to advise the Chancellor about issues of Jewish concern on the campus and in the community. During the summer of 1994, I co-chaired this task force.
  
  
• At the Jewish Community of Amherst I served on the following committees: Board of Directors, member 2002; Rabbi Search Committee, member 1987-1989; Nominating Committee, chair 1987 and member 1988; Social Concerns and Action Committee, chair 1984-1986; Education Committee, member 1976-1978 and chair 1978-1979.

Climbing the Main Coast
Heron Dance email of August 7, 2003

10. Additional Writings

• Five beer poems from the winter of 2002 can be viewed here. The first is a ditty; the second celebrates our favorite brew, Otter Creek Copper Ale; the third is postmodern; the fourth and best poem, entitled “Brewed in an Abbey Near Antwerp,” is based on true events; and the fifth is a verse-cum-quiz.
  
  
• In the fall of 2002 I wrote five additional beer poems, four of which refer to our favorite brew, Otter Creek Copper Ale. The first of the five poems is a ditty entitled “Friday Is Here”; the second was inspired by William Blake’s poem “Auguries of Innocence”; the third was inspired by Dylan Thomas’s poem “The force that through the green fuse drives the flower”; the fourth, entitled “My Sleek New Technique,” is the ultimate Otter Creek poem in which every line ends with a word rhyming with “creek”; the fifth and best, entitled “Moebius Strip,” explores the relationships between a man, his son, and his dead father.
  
  
• I wrote the lead article on the retirement of 14 faculty members in May 2002 from the Department of Mathematics and Statistics at the University of Massachusetts Amherst. The article appears on page 1, Volume 17 of the Department Newsletter for the Academic Year 2001-2002. Here is a key paragraph.

  While the effects of this exodus of 14 senior faculty members are potentially devastating, the Department will use every resource at its disposal to transform what could be a crisis into an opportunity for self-examination, restructuring, and growth. As sages from many spiritual traditions have pointed out, one’s expectations create a reality in which one’s expectations are validated. Our goal is to foster positive expectations that will create a reality in which the Department . . . continues to flourish.

• Since September 2002, I have been in charge of publicity in the Department of Mathematics and Statistics. In November 2003 my colleague, Panayotis (Panos) Kevrekidis, was selected to receive a prestigious award by the National Science Foundation’s Faculty Early Career Development (CAREER) Program. I wrote the linked article to publicize Panos’s research and excellent achievement.

Songbird Landing
The Heron Weekly #17

11a. Buddhist Spirituality

In psychological terms, both [Western psychotherapeutics and Buddhism] emphasize that what passes for normality (samsara in Buddhism) is a low-grade of psychopathology, unnoticed only because so common; that the supposedly autonomous ego-self is conditioned in ways we are normally not aware of (karma, samskaras); and that greater awareness of our mental processes can free us (samadha, prajna).

        This ability to recognize the open, empty nature of mind and all its productions, projections, thoughts, and emotions is the panacea, the universal remedy that in and of itself cures all delusion, all negative emotion, and all suffering.
       Our mind can be compared to a hand that is bound or tied up, as much by the representation of our “me,” of the ego or self, as by the conceptions and fixations belonging to this idea. Little by little, Dharma practice eliminates these self-cherishing fixations and conceptions, and, just as an unbound hand can open, the mind opens and gains all kinds of possibilities for activity. It then discovers many qualities and skills, like the hand freed from its ties. The qualities that are slowly revealed are those of enlightenment, of pure mind.

If one looks with a cold eye at the mess man has made of his history, it is difficult to avoid the conclusion that he has been affected by some built-in mental disorder which drives him towards self-destruction.

1. A Short Essay.   My short essay entitled “Automatic Pilot and the Power of the Teaching” describes an obstacle that I encountered on the way to a meditation program.
   
   
2. A Poem.   My poem “Breath” is a meditation on meditation.
   
   
   
3. Buddhism and Western Psychology.   As Buddhism unfolds in our contemporary society, what is its relationship with Western psychology? Are there areas of overlap and influence?
           These questions were asked of Joseph Goldstein in an interview published in the Fall•Winter 2003/2004 issue of Insight Newsletter. Joseph Goldstein is one of the co-founders of the Insight Meditation Society in Barre, Massachusetts. Here is his answer.

           Both Western and Buddhist psychology offer profound insight into the mind. It is helpful to understand where the two paradigms overlap, where they complement each other, and where they diverge. We can see the relationship of the two approaches clearly in the arena of afflictive emotions. This term is one translation of the Pali word kilesa, which also translates as “defilement” or “torment of mind”. I prefer “afflictive emotions” because it points directly to those mind states that cause suffering, such as depression, fear, hatred, anger, jealousy and so on — it’s a long list!
           For example, if there’s envy or jealousy arising in the mind, the first step in both Buddhist practice and Western psychology is to recognize what is arising. The second step is cultivating an acceptance of the emotion. We explore what the emotion is and practice being with it without self judgment, without condemning the state itself. So, there is recognition and acceptance — key elements common to both traditions.
           Now we come to an important difference. Buddhist teachings point to the experience and realization of anatta, or selflessness. All experience is empty of self. Within the Western psychological framework, this may be an unusual concept, with greater emphasis usually given to building-up and reinforcing the sense of self.
           The third step in working with afflictive emotions, where the Dharma can offer a unique contribution, is practicing non-identification — not taking the emotion to be “I” or “mine”. This radical view needs careful guidance and instruction. It’s not a dissociative state of denial, nor is it an unconsciousness of deep feelings. Rather, it’s the full experience of the particular mind state, but without building a superstructure of self on top of it. Each emotion arises out of conditions and is simply expressing its own nature. The “I” and “mine” are extra.

4. Practice and Fruits of Meditation.   On pages 47–48 of their book, Buddhism: A Concise Introduction, Huston Smith and Philip Novak discuss the practice and fruits of meditation.

           No teacher has credited the mind with more influence over life than the Buddha. The best loved of texts, the . . . Dhammapada, opens with the words: “All that we are is the result of what we have thought. Our life is shaped by our mind; we become what we think. Suffering follows unwholesome thought as the wheels of a cart follow the oxen that draw it. Joy follows wholesome thought like a shadow that never leaves.” And with respect to the future there is the saying: “Do you want to predict your future lives? Examine the condition of your present mind.”
           The Buddha counsels such continuous self-examination that it appears daunting, but he thought it necessary because he believed that liberation from unconscious, robotlike existence is achieved only by refined awareness. To this end he insisted that we seek to understand ourselves in depth, seeing everything in our mental and physical states as it really is. If we maintain a steady attention to our moods and thoughts, our actions and our body sensations, we perceive that they incessantly arise and disappear and are in no way permanent parts of us. Right mindfulness aims at witnessing all mental and physical events, including our emotions, without reacting to them, neither condemning some nor holding on to others.
           Through right-mindfulness practice, then, we arrive at a number of insights. We begin to see that:
           (1) every mental and physical state is in flux; none is solid or enduring;
           (2) habitual clinging to these impermanent states is at the root of much of life’s dukkha [unsatisfactoriness] and this very insight weakens the habit; and
           (3) we have little control over our mental states and our physical sensations, and normally little awareness of our reactions.
   Most important, we begin to realize that there is nobody behind the mental or physical events, orchestrating them. When the capacity for mindful attention is refined, it becomes apparent that consciousness itself is not continuous. Like the light from a lightbulb, the on/off is so rapid that consciousness seems to be steady, whereas in fact it is not. With these insights, the belief in a separate self-existent self begins to dissolve and freedom to dawn.

   
   
5. The Causal Law of Dependent Arising, the Buddha’s Greatest Contribution.   The Buddha says,“One who sees dependent arising sees the Dhamma and one who sees the Dhamma sees dependent arising.” The Dhamma is the truth discovered by the Buddha.
           In a discussion of the scientific nature of Buddhism, Huston Smith and Philip Novak discuss what the Buddha considered to be his greatest contribution: the discovery of dependent arising. The following is quoted from page 29 of their book, Buddhism: A Concise Introduction.

   Not only did it [Buddhism] make the quality of lived experience its final test, it directed its attention to discovering natural cause-and-effect relationships that affected that experience. There is no effect without its cause, and no supernatural beings who interrupt the basic causal processes of the world. The Buddha himself considered his greatest contribution to be the discovery of a causal law — dependent arising — whose short version runs, “That being present, this becomes; that not being present, this does not become.”

   On page 201 of their book, Smith and Novak present the longer version of dependent arising in its traditional formulation, followed by additional commentary.

           The longer version of dependent arising is expressed as a set of twelve interlocking conditions (nidana): (1) Ignorance (of anatta [no-self] and the Four Noble Truths) occasions (2) dispositional tendencies, which occasion (3) consciousness, which occasions (4) name and form, which occasion (5) the six sense fields, which occasion (6) contact between our senses and external reality, which occasions (7) sensations in the body and mind, which occasion (8) the entire habit structure of want ing and not wanting, which occasion (9) clinging, which occasions (10) becoming, which occasions (11) rebirth, upon which necessarily follow (12) illness, decay, death, and all their related suffering. Eradicate ignorance, says the Buddha, and the conditions of our bondage begin to fall like dominoes.
           Using these twelve conditions to explain dependent arising, however, has been likened to using the collision of a few bowling balls to explain the interactions of subatomic particles. The matter is far subtler. The all-encompassing range of dependent arising is best caught in the shorter, though deceptively simple formulation just alluded to: “When this is, that is; this arising, that arises. When this is not, that is not; this ceasing, that ceases.” This latter formulation helps us to see that dependent arising pertains not only to the human personality, but to the whole of reality. All things and events depend for their existence on other things and/or events — which resembles field theory in physics and entails as its corollary that all things and events are empty-of-own-being (anatta).

6. Indra’s Net: Teachings.   On page 61 of their book, Buddhism: A Concise Introduction, Huston Smith and Philip Novak explain dependent arising via the image of Indra’s Net, a cosmic web laced with jewels at every intersection. Concerning the implications of this image, I recommend the essay “Indra’s Postmodern Net,” a wide-reaching and profound investigation by the philosopher David Loy.

   The crux of the Buddha’s awakening was the discovery of dependent arising: every thing and every process arises in dependence upon countless other things and processes. This is the physicists’ field theory incarnate. Nothing exists on its own. Buddhists often convey this insight with the image of Indra’s Net, a cosmic web laced with jewels at every intersection. Each jewel reflects the others, together with all the reflections in the others. In the deepest analysis, each “jewel” is but the reflection of the other reflections. Likewise, every thing and every person in the world, like every jewel in Indra’s Net, because dependently arisen, is empty-of-own-being (lacking in self-existence). Empty-of-own-being is the wider meaning of anatta, applicable to the animate and inanimate world alike and less confusing than saying that “things” lack “selves.”

   The traditional description of Indra’s Net is given in the Flower Garland (Avatamsaka) Sutra. The following translation is by Francis H. Cook, Hua-yen Buddhism: The Jewel Net of Indra (University Park: The Pennsylvania State University Press, 1977), p.2.

   Far away in the heavenly abode of the great god Indra, there is a wonderful net that has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each “eye” of the net, and since the net itself is infinite in all dimensions, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring.

   According to Francis H. Cook, Indra’s Net “symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos.” Because the totality is a vast body of members each sustaining and defining all the others, “the cosmos is, in short, a self-creating, self-maintaining, and self-defining organism.” It is also non-teleological: “There is no theory of a beginning time, no concept of a creator, no question of the purpose of it all. The universe is taken as a given.” Such a universe has no hierarchy: “There is no center, or, perhaps if there is one, it is everywhere.”
   
   
7. Indra’s Net: Digital Image.   I thank Gail Atkins for allowing me to post her digital image of Indra’s Net. It is interesting to compare this image with Indra’s Net II, a computer model of the early universe in which gravity arranges matter in thin filaments.
   
   
   Indra’s Net
   Copyright © Gail Atkins
   In an email granting me permission to post her digital image of Indra’s Net on my web page, Gail Atkins made the following observation.

   “I have spent some time reading and viewing your website which shows the relatedness of mathematics, science, creativity, and both Eastern and Western philosophies.   . . . I believe that it is from the conversation among them that our greater understanding of reality will come.”

8. The Essential Mysteriousness of Our Being in the World.   In a discussion of the role of theory in Buddhism, David Loy writes the following. “The ultimate reason why there can be no ultimate theory that represents the whole is because we can never stand outside the world to re-present it objectively.” This echoes the insight of Emily Dickinson: “our entrance here being an Exclusion from comprehension” (Prose Fragment 70).

   Death being the first form of Life which we have had the power to Contemplate, our entrance here being an Exclusion from comprehension, it is amazing that the fascination of our predicament does not entice us more. With such sentences as these over our Heads we are as exempt from Exultation as the Stones —

   Here is the entire quotation by David Loy, taken from pages 26–27 of his book, The Great Awakening: A Buddhist Social Theory.

   Buddhist theory forms part of its own object domain, not only because it is a self-reflexive belief about beliefs, but because it is itself an expression of the ungraspable ground that it theorizes about. The ultimate reason why there can be no ultimate theory that represents the whole is because we can never stand outside the world to re-present it objectively. The part can never grasp or contain the whole; nor does it need to. Our concepts are not only part of the world, they are manifestations of it. Buddhist awakening does not grasp or otherwise resolve the essential mysteriousness of our being in the world. It opens us up to that mystery, a mystery that is an essential aspect of the meaning of “sacred.” In practice, this means that the broadest context for all our intel1ectual efforts is a wonder in the face of a world that always exceeds our ideas about it. That excess does not signify any defect in our understanding. Rather, it is the source of our understanding, allowing for a perpetual bubbling-up of insights and images — when we do not cling to the ones that we have already become comfortable with.

   His comment that “the broadest context for all our intel1ectual efforts is a wonder in the face of a world that always exceeds our ideas about it” resonates deeply with me.
   
   
9. Emptiness.   The following explanation appears on a web site devoted to the Buddhist teaching of sunyata, or the emptiness of things.

   [T]he Kadampa school of Buddhist philosophy claims that all things are totally empty of any defining essence. Consequently all things have no fixed identity (“inherent existence”) and are in a state of impermanence — change and flux — constantly becoming and decaying. Not only are all things constantly changing, but if we analyse any phenomenon in enough detail we come to the conclusion that it is ultimately unfindable, and exists purely by definitions in terms of other things — and one of those other things is always the mind which generates those definitions.

   David Loy points out that “the English word ‘emptiness’ has a more nihilistic connotation than the original Sanskrit sunyata. The Sanskrit root su conveys the concept of being swollen with possibility [LOY 1996].” This observation is made in the context of a discussion of the empty set, the origins of mathematics, and the Buddhist concept of sunyata or emptiness. Additional material on Buddhism and scientific rationalism and on modern Buddhism, philosophy, mathematics, and science is available.
   
   
   
10. Three Marks of Existence. To see the world in its true nature is to see the three marks of existence inherent within all things. The three marks are impermanence or anicca, suffering or dukkha, and no-self or anatta. As the on-line encyclopedia the MYSTICA points out, although each of the three marks of existence is itself a topic of meditation, they are conceptually interrelated. There is no-self because there is impermanence, and because there is impermanence, there is suffering. The generalized sense of anxiety that pervades our lives is grounded in the failure to understand the three marks of existence.

    If we examine the notion of impermanence closely and honestly, we see that it is all-pervading, [that] everything is marked by impermanence. We might posit an eternal consciousness principle, or higher self, but if we examine our consciousness closely we see that it is made up of temporary mental processes and events. We see that our “higher self” is speculative at best and imaginary to begin with. We have invented the idea to secure ourselves, to cement our relationship, once again. Because of this we feel uneasy and anxious, even at the best of times. It is only when we completely abandon clinging that we feel any relief from our queasiness.

    Our bodies are impermanent. Our lives are impermanent. We will all die. Through the awareness of death, we grow in wisdom. But as Reginald A. Ray asks on page 246 of his book, Indestructible Truth: The Living Spirituality of Tibetan Buddhism, “how can we know this not just intellectually — which has very little impact — but in our bones? Tulku Urgyen suggests that we contemplate the following analogy from Padmasambhava’s Karling Shitro.”

    Imagine that you are standing on a half-inch-wide ledge on a sheer cliff overlooking an almost bottomless abyss, with a roaring river raging below. You cannot bear to look down. Only your toes rest on the ledge, while your hands grasp two handfuls of grass the size of a goat’s beard. You are hanging onto these two handfuls of scrub-grass that represents your life span and life force. At the same time, impermanence, in the form of two rats . . . gnaws away at the grass you are clinging to, piece by piece. Once the grass is consumed, there will be nothing left to hold onto. There is only one way to go: to plunge into the nearly bottomless abyss and the raging river.   . . .   So you hang on while the rats eat up the grass, blade by blade. You have no chance of survival whatsoever. This is our current situation.

    As Rabbi Rami Shapiro writes on page 137 of his book, The Way of Solomon: Finding Joy and Contentment in the Wisdom of Ecclesiastes, the aim of meditation is “to observe the fundamental impermanence of self.”
    
    
11. Kalu Rinpoche: “We live in illusion and the appearance of things.”   In my favorite Buddhist poem Kalu Rinpoche distills the essence of the Buddhist teaching of emptiness.

    We live in illusion
    And the appearance of things.
    There is a reality.
    We are that reality.
    When you understand this,
    You see that you are nothing.
    And being nothing,
    You are everything.
    That is all.

    On page 8 of his book, A Buddhist History of the West: Studies in Lack, David Loy provides a commentary on Kalu Rinpoche’s poem.

    This process [of liberating awareness through meditation] implies that what we fear as nothingness is not really nothingness, for that is the perspective of a sense-of-self anxious about losing its grip on itself. According to Buddhism, letting go of myself into that no-thing-ness leads to something else: when consciousness stops trying to catch its own tail, I become no-thing, and discover that I am everything — or, more precisely, that I can be anything. With that conflation, the no-thing at my core is transformed from a sense of lack into a serenity that is imperturbable because there is nothing to be perturbed.

    
    “I, too, turn quiet and transparent”
    The Heron Weekly #50
    
12. The Illusion of an Unchanging Separate Identity.   The Buddha taught that suffering arises “through the misapprehension of grasping an unchanging identity which is at variance with the way things really are. . . . The principal dimension of this misapprehension is reifying ourselves into Selves, the feeling that somehow I must have an unchanging core which is the ‘Real Me’.” This quotation is taken from a cogent explanation of the Buddha’s teaching on the illusion of an unchanging separate identity. This teaching is closely related to the Buddhist understanding of the emptiness of the ego or anatta.
            Albert Einstein understood this. A rabbi wrote to Einstein, explaining that he had sought in vain to comfort his 19-year-old daughter over the death of her sister, “a sinless, beautiful, 16-year old child.” Here is Einstein’s reply.

    A human being is a part of the whole, called by us “Universe,” a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest — a kind of optical delusion of his consciousness. This delusion is a kind of prison for us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security.

13. Meditation and Transcending the “I.”   David Loy devotes his book, Lack and Transcendence: The Problem of Death and Life in Psychotherapy, Existentialism, and Buddhism, to investigating what he conjectures is the primal human repression (p. xi).

    If our sense of self as something autonomous and self-grounded is a fiction, if the ego is in fact mentally constructed and socially internalized, then perhaps our primal repression is not sexual wishes (as Freud thought) nor the fear of death (as many existential psychologists think) but the quite valid suspicion that “I” am not real.

    As David Loy explains on pages 7–8 of his book, A Buddhist History of the West: Studies in Lack, meditation is a path for transcending the sense of self. The second paragraph is also quoted in item 9.

            “Forgetting” ourselves is how we lose our sense of separation and realize that we are not other than the world. Meditation is learning how to become nothing by learning to forget the sense-of-self, which happens when I become absorbed into my meditation exercise. If the sense-of self is an effect of self-reflection — of consciousness attempting to grasp itself — such meditation practice makes sense as an exercise in de-reflection. Consciousness unlearns trying to grasp itself, real-ize itself, objectify itself. Liberating awareness occurs when the usually automatized reflexivity of consciousness ceases, which is experienced as a letting go and falling into the void. “Men are afraid to forget their minds, fearing to fall through the Void with nothing to stay their fall. They do not know that the Void is not really void, but the realm of the real dharma” (Huang-po 41). Then, when I no longer strive to make myself real through things, I find myself “actualized” by them, says Dogen.
            This process implies that what we fear as nothingness is not really nothingness, for that is the perspective of a sense-of-self anxious about losing its grip on itself. According to Buddhism, letting go of myself into that no-thing-ness leads to something else: when consciousness stops trying to catch its own tail, I become no-thing, and discover that I am everything — or, more precisely, that I can be anything. With that conflation, the no-thing at my core is transformed from a sense-of-lack into a serenity that is imperturbable because there is nothing to be perturbed.

    
    
14. The Buddha Calling the Earth To Be His Witness. During the night before his enlightenment, the Buddha was challenged by Mara, the Evil One and Buddha’s shadow-self, the lord of misfortune, sin, destruction, and death. Mara challenged the Buddha to produce witnesses to validate the Buddha’s claim that he had performed compassionate deeds. The following commentary on the Buddha’s answer appears on page 92 of Karen Armstrong‘s book, Buddha.

    But Gotama was alone; he had no human being or god on his side who could act as his witness to his long preparation for enlightenment. He therefore did something that no cakkavatti [World Ruler such as Mara] would ever do: he asked for help. Reaching out with his right hand to touch the ground, he begged the earth to testify to his past acts of compassion. With a shattering roar, the earth replied: “I bear you witness!” In terror, Mara’s elephant fell to its knees and his soldiers deserted, running in fear in all directions. The earth-witnessing posture, which shows the Buddha sitting in the cross-legged asana position, touching the ground with his right hand, is a favorite icon in Buddhist art. It not only symbolizes Gotama’s rejection of Mara’s sterile machismo, but makes the profound point that a Buddha does indeed belong to the world. The Dhamma is exacting, but it is not against nature. There is a deep affinity between the earth and the selfless human being, something that Gotama had sensed when he recalled his trance under the rose-apple tree. The man or woman who seeks enlightenment is in tune with the fundamental structure of the universe. Even though the world seems to be ruled by the violence of Mara and his army, it is the compassionate Buddha who is most truly in tune with the basic laws of existence.

    
    Buddha Calling the Earth To Be His Witness
    
15. The Buddha Under the Bodhi Tree and Salvation Mythology.   The Buddha attained enlightenment while meditating under the bodhi tree, vowing “not [to] move from this spot until I have attained the supreme and final wisdom.” The following commentary on the mythological aspects of the Buddha’s quest appears on pages 89–90 of Karen Armstrong’s book, Buddha.

    The text emphasizes the fantastic shuddering of the earth as Gotama circled the bodhi tree to remind us not to read this story literally. This is not a physical location: world-tree, standing at the axis of the cosmos, is a common feature of salvation mythology. It is the place where the divine energies pour into the world, where humanity encounters the Absolute and becomes more fully itself. We need only recall the cross of Jesus, which, according to Christian legend, stood on the same spot as the Tree of Knowledge of Good and Evil in the Garden of Eden. But in Buddhist myth, Gotama the man sits in this pivotal place, not a man-God, because human beings must save themselves without supernatural aid. The texts make it clear that Gotama had come to this axis of the universe, the mythological center that holds the whole of the cosmos together. The “immovable spot” is that psychological state which enables us to see the world and ourselves in perfect balance. Without this psychological stability and this correct orientation, enlightenment is impossible: that is why all the Buddhas had to sit in this place — or achieve this state of mind — before they were able to attain Nibbana. It is the Axis Mundi, the still point of calm where human beings, in many world myths, encounter the Real and the Unconditioned: it is the “place” where things that seem diametrically opposed in the profane world come together in that coincidentia oppositorum that constitutes an experience of the Sacred. Life and death, emptiness and plenitude, physical and spiritual merge and conjoin, like the spokes of a wheel at its hub, in a way that is unimaginable to normal consciousness. When Gotama had reached the state of perfect equilibrium that he had glimpsed as a child under the rose-apple tree, when his faculties were concentrated and his egotism under control, he was, he believed, ready to sit in the ‘immovable spot.’ He was at last in a position to receive the supreme insight.”

16. The Dhammapada.   The wisdom and compassion of the opening verses of the Dhammapada touch me deeply. Verse 1: “Our life is shaped by our mind; we become what we think.” Verse 5: “For hatred can never put an end to hatred; love alone can.” The following is taken from a website devoted to the Dhammapada.

    The Dhammapada consists of 423 verses in Pali uttered by the Buddha on some 305 occasions for the benefit of a wide range of human beings. These sayings were selected and compiled into one book as being worthy of special note on account of their beauty and relevance for moulding the lives of future generations of Buddhists. They are divided into 26 chapters and the stanzas are arranged according to subject matter.

    According to Eknath Easwaran, if all of the Buddhist sutras had been lost except the Dhammapada, it alone would be enough for readers to understand and appreciate the wisdom of the Buddha. Here are the opening six verses of the Dhammapada as translated by Eknath Easwaran.
    1. Our life is shaped by our mind; we become what we think. Suffering follows an evil thought as the wheels of a cart follow the oxen that draw it.
    2. Our life is shaped by our mind; we become what we think. Joy follows a pure thought like a shadow that never leaves.
    3. “He was angry with me, he attacked me, he defeated me, he robbed me” — those who dwell on such thoughts will never be free from hatred.
    4. “He was angry with me, he attacked me, he defeated me, he robbed me” — those who do not dwell on such thoughts will surely become free from hatred.
    5. For hatred can never put an end to hatred; love alone can. This is an unalterable law.
    6. People forget that their lives will end soon. For those who remember, quarrels come to an end.
    
    
    
    
17. The Four Noble Truths.   The Four Noble Truths are the core teaching of Buddhism, the fecund seed from which the vast orchard of the Buddha’s wisdom flowers. As Amaro Bhikkhu writes in the introduction to Food for the Heart: The Collected Teachings of Ajahn Chah, p. 23, “[t]his teaching is common to all Buddhist traditions, and just as an acorn contains within it the genetic coding for what eventually takes shape as a vast oak, so too all the myriad Buddhist teachings can be said to derive from this essential matrix of insight.” The Buddha enunciated the Four Noble Truths in a discourse given at the Deer Park at Sarnath, his first discourse after his meditation under the Bodhi tree that culminated in his enlightenment. The Four Noble Truths are the truths of suffering, the origin of suffering, the cessation of suffering, and the way leading to the cessation of suffering. As the Fourth Noble Truth explains, the way leading to the cessation of suffering is the Noble Eightfold Path. In the whimsical translation by Gary Gach and Michael Wenger, The Complete Idiot’s Guide to Understanding Buddhism, p. 80, of a passage from the Buddha’s The Flower Garland Sutra, “. . . . the Four Noble truths have four quadrillion names or meanings that are understood by sentient beings according to their tendencies. This great plethora of meaning shows all sentient beings how to gain control of their minds.”
    
    Here are an introduction and the Four Noble Truths in the translation by Venerable Ajahn Sumedho, The Four Noble Truths (Hertfordshire, England: Amaravati Publications, 1992).
    • INTRODUCTION. That both I and you have had to travel and trudge through this long round is owing to our not discovering, not penetrating four truths.
          What four? They are:
      The Noble Truth of Suffering,
          The Noble Truth of the Origin of Suffering,
      The Noble Truth of the Cessation of Suffering,
          and The Noble Truth of the Way Leading to the Cessation of Suffering.
      [Digha Nikaya, Sutta 16]
      
      
    • THE FIRST NOBLE TRUTH.   What is the Noble Truth of Suffering?
          Birth is suffering, ageing is suffering, sickness is suffering, dissociation from the loved is suffering, not to get what one wants is suffering: in short the five categories affected by clinging are suffering.
      There is this Noble Truth of Suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          This Noble Truth must be penetrated by fully understanding suffering: such was the vision, insight, wisdom, knowing, and light that arose in me about things not heard before.
      This Noble Truth has been penetrated by fully understanding suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          [Samyutta Nikaya LVI, 11]
      
      
    • THE SECOND NOBLE TRUTH.   What is the Noble Truth of the Origin of Suffering?
          It is craving which renews being and is accompanied by relish and lust, relishing this and that: in other words, craving for sensual desires, craving for being, craving for non-being.
      But whereon does this craving arise and flourish?
          Wherever there is what seems lovable and gratifying, thereon it arises and flourishes.
      There is this Noble Truth of the Origin of Suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          This Noble Truth must be penetrated to by abandoning the origin of suffering. . . .
      This Noble Truth has been penetrated to by abandoning the origin of suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          [Samyutta Nikaya LVI, 11]
      
      
    • THE THIRD NOBLE TRUTH.   What is the Noble Truth of the Cessation of Suffering?
          It is the remainderless fading and cessation of that same craving; the rejecting, relinquishing, leaving and renouncing of it.
      But whereon is this craving abandoned and made to cease?
          Wherever there is what seems lovable and gratifying, thereon it is abandoned and made to cease.
      There is this Noble Truth of the Cessation of Suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          This Noble Truth must be penetrated to by realizing the Cessation of Suffering. . . .
      This Noble Truth has been penetrated to by realising the Cessation of Suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          [Samyutta Nikaya LVI, 11]
      
      
    • THE FOURTH NOBLE TRUTH.   What is the Noble Truth of the Way Leading to the Cessation of Suffering?
          It is this Noble Eightfold Path, that is to say: Right View, Right Intention, Right Speech, Right Action, Right Livelihood, Right Effort, Right Mindfulness and Right Concentration.
      There is this Noble Truth of the Path leading to the Cessation of Suffering: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          This Noble Truth must be penetrated to by cultivating the Path....
      This Noble Truth has been penetrated to by cultivating the Path: such was the vision, insight, wisdom, knowing and light that arose in me about things not heard before.
          [Samyutta Nikaya LVI, 11]
    
    
    
18. There Are No Facts, Only Interpretations.   When Friedrich Nietzsche wrote, “There are no facts, only interpretations,” he was articulating what the Buddha had discovered 2500 years ago.
    
    
19. Meditation, Medicine for the Souls.   I found the following quote on a post near Schönbrunn Palace in Vienna in July 2004. The original German is followed by a translation.

    Meditation, MEDIZIN für die Seele. Nur das begrenzte Ich, das Ego, leidet. Das unbegrenzte Ich, das in der Stille der Meditation erfahren wird, is voll Gelassenheit, Freude, und Liebe.
    Meditation, MEDICINE for the soul. Only the constricted I, the ego, suffers. The unconstricted I, which is experienced in the stillness of meditation, is full of composure, joy, and love.

Traditional Buddha

11b. Jewish Spirituality

1. The Path of Blessing by Rabbi Marcia Prager.   Her book, entitled the PATH of BLESSING: Experiencing the Energy and Abundance of the Divine, is a profound meditation on Jewish prayer. She opens with two questions (page 11).

   If every aspect of our existence is an opportunity to experience God, how shall we live when we discover that God permeates all, from the galactic to the microscopic? How shall we respond — personally, as a society, as a species — when we begin to understand not only our lives but all existence as a sacred gift?

   Rabbi Prager’s book is an answer to these questions. The following is quoted from pages 12 and 13.

           The Hebrew word for blessing is . . . brakha . . . .   The Jewish practice of blessing derives from our tradition’s desire to promote joy and appreciation, wonder and thankfulness, amazement and praise. A brakha is, we might say, a kind of “gratitude yoga” we can employ not only day to day but moment to moment. It is in itself not at all strenuous.   . . . [I]t doesn't require that we have any accoutrements or a special mantra or that we become a yogi, an adept, a tzaddik, or a buddha. It merely asks us to engage in a moment of delayed gratification, using the respite as an opportunity for something else to occur.
           . . . [I]n making a brakha we separate out time before we consume, use, or enjoy something of the world in order to create a space where something other than thoughtless appropriation can unfold. As we grow in the path of blessing, we open to a more expansive way of being. Through blessing, we uncover the infinitely abundant Presence of God in even the smallest action.
           Jewish tradition teaches that the simple action of a brakha has a cosmic effect, for a brakha causes shefa, the “abundant flow” of God’s love and goodness, to pour into the world.

   As Rabbi Prager explains on pages 31 and 32, one approaches the act of prayer as one approaches the act of meditation, in silence and mindfully, hoping to be released from “all blemishes of ego restricting our awareness.”

           We begin in the silence that precedes any sound or movement. Jewish tradition asks that we not say a brakha until we have quieted the mind and focused our attention on the blessing’s purpose. “One should not toss a brakha from one’s mouth,” instructs the Talmud. The eleventh-century commentator Rashi adds: “A brakha should be said slowly and deliberately. Don‘t rush through as if you are carrying a heavy burden and cannot wait to be free of it!” In quiet attentiveness we focus attention and allow an opening for mindfulness.
           . . . When we quiet the mind and prepare to offer our brakha with kavvanah [focused intention], we experience an inner shift redirecting our soul toward God. We are able to gently release anxieties, feeling gratitude for the gift of this moment and the holy sparks it contains. We may wish to ask for an easing of all blemishes of ego restricting our awareness in order to deepen our praise and allow any lingering alienation and separateness to disappear.

2. Emptiness! Emptiness upon Emptiness!   In his book, The Way of Solomon: Finding Joy and Contentment in the Wisdom of Ecclesiastes, Rabbi Rami Shapiro offers a Buddhist reading of the Book of Ecclesiastes. This is apparent in the second verse, which in the King James Bible is translated as “Vanity of vanities, saith the Preacher, vanity of vanities; all [is] vanity” and in the JPS Hebrew–English Tanakh as “Utter futility! — said Koheleth — Utter futility! All is futile!” Instead Rabbi Shapiro offers the following translation, substituting the Buddhist term “emptiness” in place of “vanity” or “futility.” In this context emptiness conveys, not a meaningless void, but a dynamic, interconnected web of significance devoid of any defining essence and therefore pregnant with possibility.

   Emptiness! Emptiness upon emptiness!
   The world is fleeting of form,
   empty of permanence,
   void of surety,
   without certainty.
   Like a breath breathed once and gone,
   all things rise and fall.
   Undertand emptiness, and tranquillity replaces anxiety.
   Understand emptiness, and compassion replaces jealousy.
   Understand emptiness, and you will ceast to excuse suffering,
   and begin to alleviate it.

   In the original Hebrew the fecund, pregnant-with-possibilities phrase that yields this orchard of interpretations is havel havalim hakol havel; literally, “breath of breaths, everything is breath.” Through the lens of Rabbi Shapiro’s reading, we begin to understand the deep message of this verse. There is nothing to hold onto. All that we have is the breath. Like the breath everything is impermanent, everything is empty, everything exhibits non-self. Breath is a verb is the holy name of God is YHWH. The breath comes. The breath goes. I am being breathed.