In this profound and hopeful book, a mathematician and celebrated teacher shows how mathematics may help all of us—even the math-averse—to understand and cope with grief.
We all know the euphoria of intellectual epiphany—the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief, mathematician Michael Frame draws on a career’s worth of insight—including his work with Benoit Mandelbrot on fractal geometry—and a gift for rendering the complex accessible as he delves into this twinning of understanding and loss. Grief, Frame reveals, can be a moment of possibility.
Frame investigates grief as a response to an irrevocable change in circumstance. This reframing allows us to see parallels between the loss of a loved one or a career and the loss of the elation of first understanding a tricky concept. From this foundation, Frame builds a geometric model of mental states. An object that is fractal, for example, has symmetry of magnification: magnify a picture of a mountain or a coastline—both fractal—and we see echoes of the original shape. Similarly, nested inside great loss are smaller losses. By manipulating this geometry, Frame shows us, we may be able to redirect our thinking in ways that help reduce our pain. Small‐scale losses in essence provide laboratories to learn how to meet large-scale losses.
Interweaving original illustrations, clear introductions to advanced topics in geometry, and wisdom gleaned from his own experience with illness and others’ remarkable responses to devastating loss, Frame’s poetic book is a journey through the beautiful complexities of mathematics and life. With both human sympathy and geometrical elegance, it helps us to see how a geometry of grief can open a pathway for bold action.
In this profound and hopeful book, a mathematician and celebrated teacher shows how mathematics may help all of us—even the math-averse—to understand and cope with grief.
We all know the euphoria of intellectual epiphany—the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief, mathematician Michael Frame draws on a career’s worth of insight—including his work with Benoit Mandelbrot on fractal geometry—and a gift for rendering the complex accessible as he delves into this twinning of understanding and loss. Grief, Frame reveals, can be a moment of possibility.
Frame investigates grief as a response to an irrevocable change in circumstance. This reframing allows us to see parallels between the loss of a loved one or a career and the loss of the elation of first understanding a tricky concept. From this foundation, Frame builds a geometric model of mental states. An object that is fractal, for example, has symmetry of magnification: magnify a picture of a mountain or a coastline—both fractal—and we see echoes of the original shape. Similarly, nested inside great loss are smaller losses. By manipulating this geometry, Frame shows us, we may be able to redirect our thinking in ways that help reduce our pain. Small‐scale losses in essence provide laboratories to learn how to meet large-scale losses.
Interweaving original illustrations, clear introductions to advanced topics in geometry, and wisdom gleaned from his own experience with illness and others’ remarkable responses to devastating loss, Frame’s poetic book is a journey through the beautiful complexities of mathematics and life. With both human sympathy and geometrical elegance, it helps us to see how a geometry of grief can open a pathway for bold action.
Prologue
1
Geometry
2 Grief
3 Beauty
4 Story
5 Fractal
6 Beyond
Appendix: More Math
Acknowledgments
Notes
Index
Michael Frame retired in 2016 as adjunct professor of mathematics at Yale University. He is coauthor of Fractal Worlds: Grown, Built, and Imagined and coeditor of Benoit Mandelbrot: A Life in Many Dimensions.
"How the fractal nature of grief is both the key to understanding
it and the doorway to moving through it is what mathematician Frame
explores in his unusual book Geometry of Grief: Reflections on
Mathematics, Loss, and Life. After twenty years of working with the
visionary father of fractals and another twenty years of teaching
fractal geometry at Yale, Frame draws on a lifetime of loss and a
lifetime of delicate attention to the details of aliveness we call
beauty to interleave memoir and mathematics in an uncommon tapestry
of thought, twining Borges and quantum mechanics, evolutionary
biology and Islamic art, music and multiverse theory. . . .
Attentiveness to beauty is the instrument of transcendence—that
essential facet of Frame’s geometry of grief and readjustment."
*The Marginalian*
"Frame has written a poignant and beautiful book. . . . Treat
yourself to the wisdom of this sweet, gentle soul."
*@stevenstrogatz*
"Frame's new book, Geometry of Grief, suggests that thinking
about fractals—and thinking geometrically, in general—can help us
process life's most difficult moments... Zooming out instead of in,
we might see our individual griefs as small versions of other
tragedies in the world. Maybe, Frame says, thinking of grief as a
fractal can inspire empathy and lead us to channel our sadness into
helping others."
*Boston Globe*
"This brief, intriguing personal meditation is inspired by
mathematician Michael Frame’s lifelong love of geometry — including
20 years’ collaboration with fractal geometer Benoit Mandelbrot —
and the childhood loss of his aunt, who set him on his career path.
He writes: 'Grief informs geometry and geometry informs grief.' How
so? His epiphany on first understanding any beautiful mathematical
idea is always tinged with sadness, because it is unrepeatable.
With quirky illustrations, he integrates the lives of his Mom and
Dad."
*Nature*
"The word fractal, from the Latin fractus meaning 'broken
glass,' was coined by Benoît Mandelbrot, who brought mathematics
closer to nature by showing that iterating a simple geometric
pattern can result in complex, rough-edged, and beautiful shapes.
In Geometry of Grief, Frame, a former colleague of
Mandelbrot’s at Yale, aims to unite maths with our lived experience
still further by showing how fractals both inform and can help us
cope with the experience of irreversible loss. . . . Ambitious and
moving.”
*Times Literary Supplement*
"Frame has written a wonderful memoir. Combining his passion for
mathematics and his mastery of the geometry of fractals, in this
text he seeks to educate, encourage, and inspire readers in a
personal way. Identifying grief as irreversible, Frame makes
surprising connections to foundational mathematical concepts such
as continuity and self-similarity. . . . Here, he elucidates the
foundational intertwining of science and grief in his own life
through deeply and surprisingly personal stories from lived
experience. Weaving together references from literature, art,
popular culture, and mathematics, Frame clarifies the transcendence
found through grief as a universal human experience. The text
offers a wealth of resources for curious readers and is a must have
for the bookshelf of any mathematics teacher who wants to inspire
curiosity in students or relate with empathy to a student suffering
loss. This book will be a wonderful addition to any advanced or
graduate-level seminar, and preprofessionals in mathematics
education will certainly benefit from exploring the book's diverse
fields of discourse. Highly recommended."
*Choice*
"Frame writes: ‘Times folds up. So many ghosts crowd into my head.
Parents, grandparents, aunts and uncles, dear friends, students…
And far too many cats.’ Live long enough oneself and one realizes
that half or more of one’s friends and relatives have departed the
planet, ‘summoned,’ as the poet Robert Southey had it, ‘on the
grand tour of the universe,’ before one. One lives with it,
saddened yet grateful oneself still to be in the game. Yet some
holes never successfully fill up."
*Commentary*
“With poignancy and audacity, Frame builds an unexpected bridge
between mathematical beauty and human sorrow, illuminating
both.”
*Francis Su, author of "Mathematics for Human Flourishing"*
“I expected to enjoy the experience of thinking in fresh ways with
Frame about grief—and encountering his love of cats, really of all
nature, made manifest on the page. What blew me away were the
exciting new connections among love, grief, beauty, and resilience
that flowered in my mind as I read. Immersed in Frame’s world of
geometry, including fractals, and its applications to real-world
emotions, I sometimes felt afloat in a mysterious, and always
inviting, dream. It’s a beautiful place for all of us to spend
time.”
*Barbara J. King, author of "How Animals Grieve"*
“With concision and compassion, Frame shows how a mathematical mind
makes sense of a grieving heart. The result is a peculiar, wise,
and beautiful book.”
*Ben Orlin, author of "Math with Bad Drawings" and "Change Is the
Only Constant"*
“A unique, meaningful, and moving work that connects the
irreversibility of loss that comes with grief and the
irreversibility of first deeply understanding
something—particularly something mathematical.”
*Susan Jane Colley, Oberlin College, editor of "American
Mathematical Monthly"*
“Captured perfectly an experience that I've long tried to put into
words but couldn't—the nostalgic sense that comes immediately after
a discovery. It's astonishing how so many important ideas come to
us in an almost dream-like state, fully formed and with a hazy
beauty that somehow falls away when we more fully work out to
implications of that idea and put it into words and onto paper; the
whole process makes the idea more real but somehow less
charming."
*Christina Stankey, medical student and former student of Michael
Frame*
“Frame believes everyone can fall in love with math if it’s
presented with empathy and humor and clarity and context. He
portrays math as math-lovers know it: a beautiful garden, a place
of curiosity and delight, a tribute to human creativity and the
wonders of nature.”
*Steven Strogatz, from the foreword to "Fractal Worlds"*
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