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Геометрия скорби. Размышления о математике, об утрате близких и о жизни
Майкл Фрейм (род. 1951), математик, бывший профессор Йельского университета и коллега создателя фрактальной теории Бенуа Мандельброта, в своей книге исследует феномен скорби с точки зрения геометрии. Мы скорбим, потеряв близкого человека, домашнего питомца, прежний образ жизни – нечто любимое и важное для нас. Как могут фракталы, траектории и переменные уменьшить эту душевную боль?
По утверждению Фрейма, понимание «геометрии» своих переживаний может помочь пережить утрату. Анализируя скорбь как необратимую потерю, он обращается к законам математики, литературным сюжетам, эволюционной биологии, личному опыту. С их помощью Фрейм выводит собственные теоремы, позволяющие увидеть и проанализировать через «самоподобие» жизненного выбора, теорию мультивселенной и проецирование негативных эмоций на разные «пространства» сознания сложную закономерность чувств, составляющих скорбь.
По утверждению Фрейма, понимание «геометрии» своих переживаний может помочь пережить утрату. Анализируя скорбь как необратимую потерю, он обращается к законам математики, литературным сюжетам, эволюционной биологии, личному опыту. С их помощью Фрейм выводит собственные теоремы, позволяющие увидеть и проанализировать через «самоподобие» жизненного выбора, теорию мультивселенной и проецирование негативных эмоций на разные «пространства» сознания сложную закономерность чувств, составляющих скорбь.
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Displaying 1 - 22 of 22 reviews
June 12, 2021
There was lots of interesting geometry stuff in here, and I do like lots of interesting geometry stuff. There was also some good memoir and even a few tidbits of grief. The book did not really convince me of what it seemed to be trying to convince me of, namely that geometry could help with the grief process. I have no question that there is a geometry of grief, and even that Michael Frame has received some benefit in his own grief process with geometry, but the connections made in the book were a bit willowy for me. They were fun and interesting and sometimes hard enough to follow that I simply gave up trying to follow them, but I don't really care. When I read about grief I'm mostly interested in seeing how someone else covers themself in the swaddling rather than in seeing how they are going to help me with my own grief. And there is plenty of that here. My grief and experience are too disparate from Mr. Frame for it to make any sense as a frame-work (ha ha ha), but it works absolutely as a slit in the fabric of human experience through which I can empathize with his grief. And that's all I'm asking.
November 18, 2021
[Disclaimer: I received this book for free in exchange for an honest review via NetGalley]
Maths has been my kryptonite since day one of elementary school, which leaves me with what could be euphemistically described as a myopic view on the beauty of the subject. With the horrors of maths tests far behind me now, though, every once in a while I try to dabble in the odd popular science book for the purpose of cross-pollination - in German we say “Even a blind chicken sometimes finds a kernel”. With that in mind, I was intrigued by the concept of a book marrying the concepts of mathematics and psychology, namely confronting grief through the lens of geometry, a proposition which, if treated well, sounds like a great step in broadening your horizon.
But why would you choose to read a book about grief if you’re lucky enough not to be going through it currently? As Frame points out, grief comes in many forms and sizes and, as a highly individualized experience, you don’t need to lose a loved one to feel grief. People can grieve choices they’ve made and the doors that closed permanently as a consequence: “But many of us are haunted by thoughts of a path not taken. Some choices lead us along paths that we cannot reverse. Even if we change course now, what remains of our lives will not unfold as if we had made the other choice years earlier. What might have been is beyond our reach, and we grieve this loss.” You can even grieve the way you used to see the world before you had certain insights. I dare say most lives contain at least a modicum of those kinds of grief, and while you can never truly prepare yourself for when absolute calamity strikes, it can be an advantage to know certain tools exist and how other people employ them.
One of the aspects that strike about this book is just how likeable the author is. Deeply steeped in humbleness, the writing is refreshing and, despite the overarching mathematical theme of the book, acutely palpable to lay people, which I presume to be a direct consequence of Frame’s decades spent teaching at Yale. The theoretical parts are always kept as concise as possible, followed by a story to give practical application to what has been discussed, and in my opinion, the messages come across sharp and clear.
He dives into (and clears up) popular topics such as parallel universes and the butterfly effect, which lends a great new viewpoint on grieving.
Another aspect I highly appreciate is that Frame gives ample book recommendations for further reading.
What comes as somewhat of a relieve to me personally is the fact that in this book, geometry is the medium through which the author chooses to express his view on psychological concepts and framing techniques to deal with grief, and the real beauty of the book lies in getting a glimpse into a completely mathematical mind and its outlook, and how it pictures and processes life concepts in terms of algebra. This is absolutely fascinating to behold!
I wish the book would end a little less abruptly, I would have preferred a final musing that neatly ties the whole parcel together, but then again, I do like an author who doesn’t waffle on.
All in all, this is a marvellous quick read to expand your view on life, nature, and grief. Here some more gems:
“A notion that’s repeated often in this book is that an idea can’t be unseen. Taking in others’ ideas before thinking through my own experiences with grief might have limited how I understood those experiences. […] The first step is to understand your own experience, then see how it fits into established works.”
“When I see something beautiful, that first realization is tinged with grief, because I know I’ll never again feel so strongly about it. When I see something pretty, there is no initial gasp like the gasp that accompanies the first glimpse of beauty. Subsequent viewings of the same pretty thing can produce about the same pleasure. We feel no grief, because our initial impression is reproducible.”
“I focused on the actions, not the feelings, and imagined other people helping their neighbours in similar ways. I saw what Dad did […] as part of a larger picture. Even though he would not do this again, the idea, the movement, of neighbour helping neighbour, to which Dad belonged, would continue. Projection to the space of neighbour helping neighbour eased the grief.”
“Death closes the door to the further experiences with those we have irreversibly lost. But grief opens a door, maybe just a crack, to let us remix memories, see actions in a new way. Let us think what the person who has died would want us to do. Examples are familiar: “In lieu of flowers, the family suggests a donation to…” […] A cause dear to the person who has died gets a boost in their memory. Their influence still is felt.”
Maths has been my kryptonite since day one of elementary school, which leaves me with what could be euphemistically described as a myopic view on the beauty of the subject. With the horrors of maths tests far behind me now, though, every once in a while I try to dabble in the odd popular science book for the purpose of cross-pollination - in German we say “Even a blind chicken sometimes finds a kernel”. With that in mind, I was intrigued by the concept of a book marrying the concepts of mathematics and psychology, namely confronting grief through the lens of geometry, a proposition which, if treated well, sounds like a great step in broadening your horizon.
But why would you choose to read a book about grief if you’re lucky enough not to be going through it currently? As Frame points out, grief comes in many forms and sizes and, as a highly individualized experience, you don’t need to lose a loved one to feel grief. People can grieve choices they’ve made and the doors that closed permanently as a consequence: “But many of us are haunted by thoughts of a path not taken. Some choices lead us along paths that we cannot reverse. Even if we change course now, what remains of our lives will not unfold as if we had made the other choice years earlier. What might have been is beyond our reach, and we grieve this loss.” You can even grieve the way you used to see the world before you had certain insights. I dare say most lives contain at least a modicum of those kinds of grief, and while you can never truly prepare yourself for when absolute calamity strikes, it can be an advantage to know certain tools exist and how other people employ them.
One of the aspects that strike about this book is just how likeable the author is. Deeply steeped in humbleness, the writing is refreshing and, despite the overarching mathematical theme of the book, acutely palpable to lay people, which I presume to be a direct consequence of Frame’s decades spent teaching at Yale. The theoretical parts are always kept as concise as possible, followed by a story to give practical application to what has been discussed, and in my opinion, the messages come across sharp and clear.
He dives into (and clears up) popular topics such as parallel universes and the butterfly effect, which lends a great new viewpoint on grieving.
Another aspect I highly appreciate is that Frame gives ample book recommendations for further reading.
What comes as somewhat of a relieve to me personally is the fact that in this book, geometry is the medium through which the author chooses to express his view on psychological concepts and framing techniques to deal with grief, and the real beauty of the book lies in getting a glimpse into a completely mathematical mind and its outlook, and how it pictures and processes life concepts in terms of algebra. This is absolutely fascinating to behold!
I wish the book would end a little less abruptly, I would have preferred a final musing that neatly ties the whole parcel together, but then again, I do like an author who doesn’t waffle on.
All in all, this is a marvellous quick read to expand your view on life, nature, and grief. Here some more gems:
“A notion that’s repeated often in this book is that an idea can’t be unseen. Taking in others’ ideas before thinking through my own experiences with grief might have limited how I understood those experiences. […] The first step is to understand your own experience, then see how it fits into established works.”
“When I see something beautiful, that first realization is tinged with grief, because I know I’ll never again feel so strongly about it. When I see something pretty, there is no initial gasp like the gasp that accompanies the first glimpse of beauty. Subsequent viewings of the same pretty thing can produce about the same pleasure. We feel no grief, because our initial impression is reproducible.”
“I focused on the actions, not the feelings, and imagined other people helping their neighbours in similar ways. I saw what Dad did […] as part of a larger picture. Even though he would not do this again, the idea, the movement, of neighbour helping neighbour, to which Dad belonged, would continue. Projection to the space of neighbour helping neighbour eased the grief.”
“Death closes the door to the further experiences with those we have irreversibly lost. But grief opens a door, maybe just a crack, to let us remix memories, see actions in a new way. Let us think what the person who has died would want us to do. Examples are familiar: “In lieu of flowers, the family suggests a donation to…” […] A cause dear to the person who has died gets a boost in their memory. Their influence still is felt.”
August 12, 2022
Può la geometria insegnarci qualcosa su come si supera il dolore? Da questa domanda che pare accostare concetti incongrui parte il libro di Michael Frame, matematico esperto di frattali, allievo di Mandelbrot e che sui frattali ha pubblicato libri molto belli e che forse varrebbe la pena tradurre in italiano.
Perché mai la geometria dovrebbe insegnarci qualcosa sul dolore? Perché, argomenta Frame, ogni dolore è conseguenza di uno strappo, ogni lutto è una perdita di continuità, potremmo dire,
Tale perdita di continuità, ci dice Frame, è però spesso apparente, ci sembra tale solo perché proiezione su di uno spazio esistenziale limitato a poche coordinate di un oggetto multidimensionale complesso. Ora: se non avete idee sulla geometria a molte dimensioni questo non è semplicissimo da spiegare, lo spiega lui e non ho bisogno di spiegarlo io. Inoltre il dolore, proprio come i frattali, presenta una specifica invarianza di scala: i dolori di grandi perdite assomigliano tantissimo ai dolori delle piccole perdite. L'autore suggerisce allora di muoversi con coscienza lungo diverse scale spaziali e temporali per riuscire a lenire questi dolori. Va preso per quel che è; forse una raffinata metafora, forse un autoinganno, di certo una possibile ricerca di senso, usando l'immaginazione spaziale di un matematica, di quello che ci attraversa. E l'autore è perfettamente cosciente di non aver trovato una chiave universale che affranchi l'uomo dalle sue paure. Si tratta, piuttosto, di uno specifico viaggio intellettuale in cui con modestia e intelligenza l'autore ripercorre alcuni momenti dolorosi della sua esistenza e riconosce il modo in cui la sua formazione matematica ha contributo a dar loro forma.
Non c'è solo dolore in queste pagine. Un intero capitolo sulla universalità della bellezza, ad esempio, con la sua delicata miscela di sorpresa e riconoscimento, restituisce uno sguardo contemporaneamente scientifico ed empatico sul mondo.
A toccare di più, però, sono le parole lievi con cui ricorda la figura del padre e il suo funerale, o la fine prevista ma non per questo meno dolorosa del gatto Skyzzy. Anche il sommesso e costante rimpianto per aver dovuto lasciare l'insegnamento universitario con un po' di anticipo per problemi di salute.
Non manca, ovviamente, la matematica e, tra le sue illustrazioni piacevolmente amatoriali che tanto ricordano i maldestri tentativi di tante lezioni, trovano spazio dimostrazioni eleganti e una splendida appendice in grado di trascinare in poche righe da un quadrato ad aspetti non banali della
geometria dei frattali aleatori.
Campeggia, quasi ovunque, quel triangolo di Sierpinski che non può fare cortocircuito, nella mia mente, con il capolavoro di DFW, Infinite Jest, programmaticamente scritto a forma di frattale che, con il suo oculato alternare di presenze e rimozioni mette in scena altre e diversissime parabole di gestione della sofferenza, basata sullo sport, sulla fuga, sulla dipendenza.
Riflessioni che aiutano a definire il perimetro della matematica riportata alla sua dimensione di esperienza umana.
Perché mai la geometria dovrebbe insegnarci qualcosa sul dolore? Perché, argomenta Frame, ogni dolore è conseguenza di uno strappo, ogni lutto è una perdita di continuità, potremmo dire,
Tale perdita di continuità, ci dice Frame, è però spesso apparente, ci sembra tale solo perché proiezione su di uno spazio esistenziale limitato a poche coordinate di un oggetto multidimensionale complesso. Ora: se non avete idee sulla geometria a molte dimensioni questo non è semplicissimo da spiegare, lo spiega lui e non ho bisogno di spiegarlo io. Inoltre il dolore, proprio come i frattali, presenta una specifica invarianza di scala: i dolori di grandi perdite assomigliano tantissimo ai dolori delle piccole perdite. L'autore suggerisce allora di muoversi con coscienza lungo diverse scale spaziali e temporali per riuscire a lenire questi dolori. Va preso per quel che è; forse una raffinata metafora, forse un autoinganno, di certo una possibile ricerca di senso, usando l'immaginazione spaziale di un matematica, di quello che ci attraversa. E l'autore è perfettamente cosciente di non aver trovato una chiave universale che affranchi l'uomo dalle sue paure. Si tratta, piuttosto, di uno specifico viaggio intellettuale in cui con modestia e intelligenza l'autore ripercorre alcuni momenti dolorosi della sua esistenza e riconosce il modo in cui la sua formazione matematica ha contributo a dar loro forma.
Non c'è solo dolore in queste pagine. Un intero capitolo sulla universalità della bellezza, ad esempio, con la sua delicata miscela di sorpresa e riconoscimento, restituisce uno sguardo contemporaneamente scientifico ed empatico sul mondo.
A toccare di più, però, sono le parole lievi con cui ricorda la figura del padre e il suo funerale, o la fine prevista ma non per questo meno dolorosa del gatto Skyzzy. Anche il sommesso e costante rimpianto per aver dovuto lasciare l'insegnamento universitario con un po' di anticipo per problemi di salute.
Non manca, ovviamente, la matematica e, tra le sue illustrazioni piacevolmente amatoriali che tanto ricordano i maldestri tentativi di tante lezioni, trovano spazio dimostrazioni eleganti e una splendida appendice in grado di trascinare in poche righe da un quadrato ad aspetti non banali della
geometria dei frattali aleatori.
Campeggia, quasi ovunque, quel triangolo di Sierpinski che non può fare cortocircuito, nella mia mente, con il capolavoro di DFW, Infinite Jest, programmaticamente scritto a forma di frattale che, con il suo oculato alternare di presenze e rimozioni mette in scena altre e diversissime parabole di gestione della sofferenza, basata sullo sport, sulla fuga, sulla dipendenza.
Riflessioni che aiutano a definire il perimetro della matematica riportata alla sua dimensione di esperienza umana.
June 18, 2022
I didn’t understand everything in this book. It’s been quite a while since I’ve had to consider x and y axes. But that didn’t really matter. What I took from this book is that the way we see the world informs the way we think. And for the most part, Euclidean geometry determines the way we see the world. But there are other ways to frame your understanding of the world around you (fractal geometry) and other ways to frame grief. There is no cure for the inevitable sadness of irreversible loss but there are different ways to think about it to alter the way it overwhelms. And also, the authors name is “Frame.” Good one, universe.
April 18, 2021
Frame did not convince me of the relatedness of geometry and grief, but I’d watch a dialectic about it - or his Ted talk if he gave one. The book is lovely and moving.
March 9, 2024
2.5/5
DNF; i can’t even bring myself to finish reading. the premise of this book is beautiful, paralleling the process of grief to mathematical concepts and the process of working through math problems. author maybe just doesn’t really write in an interesting way. many pointless sentences or meaningless words within sentences. i had high hopes for it and thought maybe it would help me process the loss of a friend but maybe you don’t ever really figure that out do you
DNF; i can’t even bring myself to finish reading. the premise of this book is beautiful, paralleling the process of grief to mathematical concepts and the process of working through math problems. author maybe just doesn’t really write in an interesting way. many pointless sentences or meaningless words within sentences. i had high hopes for it and thought maybe it would help me process the loss of a friend but maybe you don’t ever really figure that out do you
September 14, 2021
‘’In the dark hours between midnight and dawn, we are alone with our thoughts. This is when we best sift through our personal grief.’’
Geometry of grief is a book with a fascinating concept, written by mathematician Michael Frame. With the book, the author tries to provide the reader with parallels between geometry and grief in a hope this might help to cope with situations of severe grief.
The books starts very promising with many beautifully written description of grief and the complexity of the emotion/situation. A citation:
‘’Grief is a response to an irreversible loss. A corollary: there is no anticipatory grief. To generate grief rather than sadness, the thing lost must carry great emotional weight, and it must pull back the veil that covers a transcendent aspect of the world.’’
As a mental health professional (physician), I found this part of the book very readable and relatable, yet at the same time honest, personal and philosophical.
But than I got lost. The author writes ‘’You may feel that we’ve wondered a long way from thoughts of grief, but we haven’t.’’ I personally just couldn’t follow. The author makes extensive parallels between geometry, or more general mathematics, and patterns of a grief response. Maybe I’m just not passionate enough about maths or maybe it’s been too long since I did abstract maths myself, but I got hopelessly lost.
In the final chapters of the book the authors sums it up very well with the combination of the combination of the following two sentences:
‘’Now I don’t know if this approach will be of use to someone whose thinking is not primarily geometrical or visual’’.
And
‘’We cannot enter the personal hell of another, but we can imagine our hell if we inhabited their situation’’.
I think it’s exactly that: this book is an amazing tool for those that try to create an order into the chaos, but in the way which for many others seems very abstract: through geometry. I think I just wasn’t the right target audience, and sincerely hope this book will find the right readers. Because grief is a heartbreaking process and anyone out there struggling should be able to find a relatable tool to guide and feel less alone.
Disclaimer: I received an ARC from NetGalley in exchange for a review.
Geometry of grief is a book with a fascinating concept, written by mathematician Michael Frame. With the book, the author tries to provide the reader with parallels between geometry and grief in a hope this might help to cope with situations of severe grief.
The books starts very promising with many beautifully written description of grief and the complexity of the emotion/situation. A citation:
‘’Grief is a response to an irreversible loss. A corollary: there is no anticipatory grief. To generate grief rather than sadness, the thing lost must carry great emotional weight, and it must pull back the veil that covers a transcendent aspect of the world.’’
As a mental health professional (physician), I found this part of the book very readable and relatable, yet at the same time honest, personal and philosophical.
But than I got lost. The author writes ‘’You may feel that we’ve wondered a long way from thoughts of grief, but we haven’t.’’ I personally just couldn’t follow. The author makes extensive parallels between geometry, or more general mathematics, and patterns of a grief response. Maybe I’m just not passionate enough about maths or maybe it’s been too long since I did abstract maths myself, but I got hopelessly lost.
In the final chapters of the book the authors sums it up very well with the combination of the combination of the following two sentences:
‘’Now I don’t know if this approach will be of use to someone whose thinking is not primarily geometrical or visual’’.
And
‘’We cannot enter the personal hell of another, but we can imagine our hell if we inhabited their situation’’.
I think it’s exactly that: this book is an amazing tool for those that try to create an order into the chaos, but in the way which for many others seems very abstract: through geometry. I think I just wasn’t the right target audience, and sincerely hope this book will find the right readers. Because grief is a heartbreaking process and anyone out there struggling should be able to find a relatable tool to guide and feel less alone.
Disclaimer: I received an ARC from NetGalley in exchange for a review.
April 30, 2023
As others mentioned, the book doesn't deliver what it promises, but instead, it is full of all kinds of interesting stuff, and the mind of the writer walks abound beautifully. This is part of the book that I liked a lot:
"I thought gravity pulled my mind into the past, stuck in memories. But now I know I can’t trust memories. Some are invented, all are edited. The whole web of who I am—what I’ve seen and done, what skills I’ve found—is nothing but fog. Gravity pulls me to the future, bits of me falling off along the way. Each of us disappears into the mist of the possible. In our minds, time is gravity’s other side. In the last moments before I vanish, will I see you again? Only one moment, one glimpse, is all I want. All I need. As my memory dissolves, is there no chance to see you, touch your face, hold your hand, see my face reflected in your eyes? Why can’t I stop weeping? Why can’t I find my breath? Everything is so small and dark. I hope I see you before I finish writing thi"
"I thought gravity pulled my mind into the past, stuck in memories. But now I know I can’t trust memories. Some are invented, all are edited. The whole web of who I am—what I’ve seen and done, what skills I’ve found—is nothing but fog. Gravity pulls me to the future, bits of me falling off along the way. Each of us disappears into the mist of the possible. In our minds, time is gravity’s other side. In the last moments before I vanish, will I see you again? Only one moment, one glimpse, is all I want. All I need. As my memory dissolves, is there no chance to see you, touch your face, hold your hand, see my face reflected in your eyes? Why can’t I stop weeping? Why can’t I find my breath? Everything is so small and dark. I hope I see you before I finish writing thi"
January 7, 2022
This is a unique take on the parallels of geometry & grief. Only a true, devoted geometer could have created this intriguing piece of work. Dr. Frame's sucess both as a teacher & an author stems from empathy towards his students and readers. He has successfully presented a complicated subject in witty, funny & engaging manner, supported by his personal life incidents & insights. He also provides a rich reference section, many of the books in which are now on my to-read list. So glad to have come across this masterful work.
October 29, 2022
This book convinced me that there's no such thing as geometry of grief.
June 19, 2023
I want to cry. Do you know how good a math book needs to be to make me cry? (I say this as if I haven’t cried over the housekeeper and the professor but still. ) favorite. I just. I.
September 28, 2023
Ridiculously the title in Korean is 'The Consolation of Mathematics'.
Even though I was not able to understand some detailed parts about mathematics,
General structure was quite clear.
It's about relationship between grief and geometry, and the medium is, I guess, beauty and being in irretrievable situation.
The different side of grief from other sad feeling is 'being irretrievable' from losing someone.
He usually talks about his experience when his family passes away.
On the other hand, even when we learn something, or we meet 'A-ha' moments, we can not go back before we didn't know the moment.
Beauty is same. I was not to caught by the 'beauty' in this book though, still there is space for beauty in geometry and even grief.
As a reader, still I can not understand clearly the relationship between them and If it's true.
Roughly speaking, everything is irretrievable. If I learn some languages, It's totally different from the former version of me, and still it's beautiful to learn them. But we don't think learning language is similar as geometry. mmmm, I mean, It's not a critical point at least.
Despite of some connecting point that I cannot understand,
The thing I like is his approach. He just doesn't autopsy the concept of grief 'mathematically'.
Rather it is close to it of philosophers. He describes his moments of grief as a person.
I always like the point. Moreover, he exhibits kind of wisdom on a problem in life.
Life can be treated by a fractal structure, which means same patterns repeat endlessly in an existence. Irretrievable things in a smaller time also keep happening, so I can practice on treating grief. When he lost his cat, He found out many memories of his cat still remained around his house, including neighbors. Now he always helps cats to survive.
Let's rate some points for fun. It doesn't mean the book's value itself anyway.
Do I understand this book enough? So-So.(3)
Was this book so helpful? Quite.(3.5)
Do I like this book at the moments when I was reading? Yes.(4)
Will I reread this book someday? Possible. (2.5)
-> 3.2 average points
and seperately considering that I couldn't count... (+0.3)
-> 3.5 (average points).
How stupid I am...
Even though I was not able to understand some detailed parts about mathematics,
General structure was quite clear.
It's about relationship between grief and geometry, and the medium is, I guess, beauty and being in irretrievable situation.
The different side of grief from other sad feeling is 'being irretrievable' from losing someone.
He usually talks about his experience when his family passes away.
On the other hand, even when we learn something, or we meet 'A-ha' moments, we can not go back before we didn't know the moment.
Beauty is same. I was not to caught by the 'beauty' in this book though, still there is space for beauty in geometry and even grief.
As a reader, still I can not understand clearly the relationship between them and If it's true.
Roughly speaking, everything is irretrievable. If I learn some languages, It's totally different from the former version of me, and still it's beautiful to learn them. But we don't think learning language is similar as geometry. mmmm, I mean, It's not a critical point at least.
Despite of some connecting point that I cannot understand,
The thing I like is his approach. He just doesn't autopsy the concept of grief 'mathematically'.
Rather it is close to it of philosophers. He describes his moments of grief as a person.
I always like the point. Moreover, he exhibits kind of wisdom on a problem in life.
Life can be treated by a fractal structure, which means same patterns repeat endlessly in an existence. Irretrievable things in a smaller time also keep happening, so I can practice on treating grief. When he lost his cat, He found out many memories of his cat still remained around his house, including neighbors. Now he always helps cats to survive.
Let's rate some points for fun. It doesn't mean the book's value itself anyway.
Do I understand this book enough? So-So.(3)
Was this book so helpful? Quite.(3.5)
Do I like this book at the moments when I was reading? Yes.(4)
Will I reread this book someday? Possible. (2.5)
-> 3.2 average points
and seperately considering that I couldn't count... (+0.3)
-> 3.5 (average points).
How stupid I am...
October 31, 2022
I picked up this book at the MIT Press Bookstore when we were out in Boston earlier this month.
This is a short work, but by no means a lightweight read. A mathematician, whose focus has been on the geometry of fractals, ponders the subject of grief, drawing on geometric ideas as guiding metaphors.
Grief has been a baffling struggle for me over the course of my life. Rather than being desensitized by each new loss, the sadness seems to deepen with each occurrence. Indeed, some of the stories of loss that Frame relates left me in tears.
Whatever reassurance religious faith might have offered has long subsided with my disillusionment toward religion in general. I have read other books and articles on loss, but I haven't seen a work that gave me something to work with convincingly.
It will be a while and lots of additional reflection before I have a feel for whether this book will have a lasting impact, but I am optimistic. Frame provides an honest exploration of the inevitability of grief and sketches out how we can use the idea of stories and viewpoints to channel that grief into meaning.
Frame is someone who loves mathematics deeply, but he is well read and well rounded. He draws upon both mathematical and non-mathematical sources to make his points, and he cites examples of where others in literature and arts have made similar points. With humility, he notes that what worked for him in his experiences may not translate readily to the experiences of others.
There is a lot of math, much of it beyond high school level, but it is discussed at a very accessible level. Gory details for the more rigorously minded are saved for a brief appendix and footnotes. The math is used both to describe his lifelong love of the subject and how it can be used to give richer context to the narratives of our lives. If anything, you'll get a quick refresher of what that fuss over fractals was about 30 or 40 years ago. He was at the forefront of that, collaborating with Benoit Mandelbrot.
This is a short work, but by no means a lightweight read. A mathematician, whose focus has been on the geometry of fractals, ponders the subject of grief, drawing on geometric ideas as guiding metaphors.
Grief has been a baffling struggle for me over the course of my life. Rather than being desensitized by each new loss, the sadness seems to deepen with each occurrence. Indeed, some of the stories of loss that Frame relates left me in tears.
Whatever reassurance religious faith might have offered has long subsided with my disillusionment toward religion in general. I have read other books and articles on loss, but I haven't seen a work that gave me something to work with convincingly.
It will be a while and lots of additional reflection before I have a feel for whether this book will have a lasting impact, but I am optimistic. Frame provides an honest exploration of the inevitability of grief and sketches out how we can use the idea of stories and viewpoints to channel that grief into meaning.
Frame is someone who loves mathematics deeply, but he is well read and well rounded. He draws upon both mathematical and non-mathematical sources to make his points, and he cites examples of where others in literature and arts have made similar points. With humility, he notes that what worked for him in his experiences may not translate readily to the experiences of others.
There is a lot of math, much of it beyond high school level, but it is discussed at a very accessible level. Gory details for the more rigorously minded are saved for a brief appendix and footnotes. The math is used both to describe his lifelong love of the subject and how it can be used to give richer context to the narratives of our lives. If anything, you'll get a quick refresher of what that fuss over fractals was about 30 or 40 years ago. He was at the forefront of that, collaborating with Benoit Mandelbrot.
December 22, 2023
This book was introduced to me by someone I love and have great admiration for. This person has been given more than their fair portion of grief, and more than anyone I've met experiences this grief in a fractious state of thoughts and emotions, yet is one of the strongest and bravest people you would ever meet. Based on discussing the mere presence of this book, I sought to understand the analogy of fractals and fractal states of the psyche, such as broken memories, and grief.
Unfortunately this book wasn't (for me) of any real value.
As I mentioned in progress updates, this book is based quite a bit on the author's personal experiences. These won't map perfectly well to everyone. There is a fair amount of math and geometry explained in a minimal way. The core concept, that of relating to grief is something that can be adjusted or scaled to fit, is ultimately explained haphazardly. I am a visual and literal reader, and I would have appreciated illustrations that explained the core concept, and not just the geometric ones.
Unfortunately this book wasn't (for me) of any real value.
As I mentioned in progress updates, this book is based quite a bit on the author's personal experiences. These won't map perfectly well to everyone. There is a fair amount of math and geometry explained in a minimal way. The core concept, that of relating to grief is something that can be adjusted or scaled to fit, is ultimately explained haphazardly. I am a visual and literal reader, and I would have appreciated illustrations that explained the core concept, and not just the geometric ones.
May 18, 2021
We are certainly in a moment where the world has suffered trauma and is going through quite a bit of grief. So it’s understandable that many people would want to read about different perspectives on grief. And there are countless books, ranging from deep philosophical tomes to cheesy self-help books, that discuss what it means to grieve. But I strongly suspect this is the only one that ties the grieving process to The Simpsons, Natalie Merchant, Salvador Dali, and fractal geometry.
Frame mostly discusses the grief of geometry and what he dubs the geometry of grief, delving into lots of abstract mathematical ideas in an attempt to explain the connections with the topic. I can’t say he fully convinces me, but the book is lovely to read and very thought provoking and I certainly think many people will learn a lot from this, whether it is Mathematics or Psychology or maybe some of each.
Frame mostly discusses the grief of geometry and what he dubs the geometry of grief, delving into lots of abstract mathematical ideas in an attempt to explain the connections with the topic. I can’t say he fully convinces me, but the book is lovely to read and very thought provoking and I certainly think many people will learn a lot from this, whether it is Mathematics or Psychology or maybe some of each.
June 22, 2025
A Tender and Thoughtful Blend of Math and Mourning
Michael Frame’s Geometry of Grief is a beautifully written meditation that weaves together mathematics, personal loss, and philosophy. Drawing from his life as a mathematician and his experiences with grief, Frame offers reflections that are both intellectually engaging and emotionally resonant. His exploration of fractals and non-linearity as metaphors for the grieving process is especially moving.
While some mathematical sections may feel dense for general readers, they are presented with enough clarity and care to be accessible to most. At times, the tone leans heavily academic, but this is balanced by sincere vulnerability and poetic insights.
A unique and poignant book—perfect for those who find solace in the intersection of reason and emotion.
Michael Frame’s Geometry of Grief is a beautifully written meditation that weaves together mathematics, personal loss, and philosophy. Drawing from his life as a mathematician and his experiences with grief, Frame offers reflections that are both intellectually engaging and emotionally resonant. His exploration of fractals and non-linearity as metaphors for the grieving process is especially moving.
While some mathematical sections may feel dense for general readers, they are presented with enough clarity and care to be accessible to most. At times, the tone leans heavily academic, but this is balanced by sincere vulnerability and poetic insights.
A unique and poignant book—perfect for those who find solace in the intersection of reason and emotion.
November 27, 2023
A beautiful synopsis of Mathematics, Grief, and Beauty.
While not thoroughly showing the connection between the three, Frame does a good job showing their similarities and how they bounce off of each other. This book has given me a new outlook on life.
However, after making a point Frame tends to ramble on a bit on things that are hard to follow. Reading his bit on space projection was a bit confusing, and I think he could've done a better job explaining that concept. Especially since the books conclusion came to that.
While not thoroughly showing the connection between the three, Frame does a good job showing their similarities and how they bounce off of each other. This book has given me a new outlook on life.
However, after making a point Frame tends to ramble on a bit on things that are hard to follow. Reading his bit on space projection was a bit confusing, and I think he could've done a better job explaining that concept. Especially since the books conclusion came to that.
January 25, 2024
Very practical. I don’t really get emotion from the author. And when I do, it’s about dead cats. Nothing really revolutionary. I don’t know if I agree with the author’s assumption: the best way to respond to grief is to minimize anguish.
December 23, 2024
This book seemed like an interesting idea, so I picked it up. To be totally honest, though, I don't feel like there's anything but a loose degree connection between grief and geometry, even after reading this book.
February 20, 2025
3.5⭐️ read! Couple ideas in here I loved, but I wish the book felt more cohesive. I don’t think Frame really succeeds in marrying geometry and grief. There are moments of connection but it doesn’t quite come together.
July 12, 2025
I couldn't grasp a majority of what he was trying to convey. some of the fractal chapter resonated, but otherwise I'm left with this thought.... huh?
January 13, 2025
Completely original but more a look into a new perspective. Might not find anything to transpose unto your own life
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