What do you think?
Rate this book
The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality
The New York Times Book Review Editors' Choice • A poet, a physicist, and a philosopher explored the greatest enigmas in the universe—the nature of free will, the strange fabric of the cosmos, the true limits of the mind—and each in their own way uncovered a revelatory truth about our place in the world
“[A] mind-expanding book. . . . Elegantly written.” — The New York Times
Argentine poet Jorge Luis Borges was madly in love when his life was shattered by painful heartbreak. But the breakdown that followed illuminated an incontrovertible truth—that love is necessarily imbued with loss, that the one doesn’t exist without the other. German physicist Werner Heisenberg was fighting with the scientific establishment on the meaning of the quantum realm’s absurdity when he had his own epiphany—that there is no such thing as a complete, perfect description of reality. Prussian philosopher Immanuel Kant pushed the assumptions of human reason to their mind-bending conclusions, but emerged with an idea that crowned a towering philosophical system—that the human mind has fundamental limits, and those limits undergird both our greatest achievements as well as our missteps.
Through fiction, science, and philosophy, the work of these three thinkers coalesced around the powerful, haunting fact that there is an irreconcilable difference between reality “out there” and reality as we experience it. Out of this profound truth comes a multitude of galvanizing the notion of selfhood, free will, and purpose in human life; the roots of morality, aesthetics, and reason; and the origins and nature of the cosmos itself.
As each of these thinkers shows, every one of us has a fundamentally incomplete picture of the world. But this is to be expected. Only as mortal, finite beings are we able to experience the world in all its richness and breathtaking majesty. We are stranded in a gulf of vast extremes, between the astronomical and the quantum, an abyss of freedom and absolute determinism, and it is in that center where we must make our home. A soaring and lucid reflection on the lives and work of Borges, Heisenberg, and Kant, The Rigor of Angels movingly demonstrates that the mysteries of our place in the world may always loom over us—not as a threat, but as a reminder of our humble humanity.
“[A] mind-expanding book. . . . Elegantly written.” — The New York Times
Argentine poet Jorge Luis Borges was madly in love when his life was shattered by painful heartbreak. But the breakdown that followed illuminated an incontrovertible truth—that love is necessarily imbued with loss, that the one doesn’t exist without the other. German physicist Werner Heisenberg was fighting with the scientific establishment on the meaning of the quantum realm’s absurdity when he had his own epiphany—that there is no such thing as a complete, perfect description of reality. Prussian philosopher Immanuel Kant pushed the assumptions of human reason to their mind-bending conclusions, but emerged with an idea that crowned a towering philosophical system—that the human mind has fundamental limits, and those limits undergird both our greatest achievements as well as our missteps.
Through fiction, science, and philosophy, the work of these three thinkers coalesced around the powerful, haunting fact that there is an irreconcilable difference between reality “out there” and reality as we experience it. Out of this profound truth comes a multitude of galvanizing the notion of selfhood, free will, and purpose in human life; the roots of morality, aesthetics, and reason; and the origins and nature of the cosmos itself.
As each of these thinkers shows, every one of us has a fundamentally incomplete picture of the world. But this is to be expected. Only as mortal, finite beings are we able to experience the world in all its richness and breathtaking majesty. We are stranded in a gulf of vast extremes, between the astronomical and the quantum, an abyss of freedom and absolute determinism, and it is in that center where we must make our home. A soaring and lucid reflection on the lives and work of Borges, Heisenberg, and Kant, The Rigor of Angels movingly demonstrates that the mysteries of our place in the world may always loom over us—not as a threat, but as a reminder of our humble humanity.
368 pages, Hardcover
Published August 29, 2023
About the author
William Egginton
22 books48 followersWilliam Egginton is a literary critic and philosopher. He has written extensively on a broad range of subjects, including theatricality, fictionality, literary criticism, psychoanalysis and ethics, religious moderation, and theories of mediation. William Egginton was born in Syracuse, New York in 1969. He received his PhD in Comparative Literature from Stanford University in 1999. His doctoral thesis, "Theatricality and Presence: a Phenomenology of Space and Spectacle in Early Modern France and Spain," was written under the direction of Hans Ulrich Gumbrecht. He currently resides with his wife, Bernadette Wegenstein, and their three children, in Baltimore, Maryland. William Egginton is the Decker Professor in the Humanities and Director of the Alexander Grass Humanities Institute at the Johns Hopkins University, where he teaches on Spanish and Latin American literature, literary theory, and the relation between literature and philosophy.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 132 reviews
December 22, 2023
Reality is a collective, hallucinated construct.
I don’t read much philosophy but I read lots, and have studied, quantum mechanics. The Rigor of Angels is a beautiful crossroads of three great thinkers, Kant, Borges and Heisenberg and their attempts to explain the inexplicable. What I mean is, when we dive down onto the quantum level and compare it to the macro level, the underpinnings of our assumptions about reality disappear. The more you study the expanse of the universe and down to the quantum level, any harmony about how reality is cobbled together makes absolutely no sense. On the quantum level, there are no “things” only probability wave forms that come into existence when we look at them. How can matter and the macro world, something to us that is tangible and immutable, be made of something that kind of is and isn’t there?
This is the paradox that has vexed many people, including Einstein and Schrodinger, ever since observations and mathematics of quantum mechanics happened. What the author does in this book is assert a central thesis: we cannot understand how to harmonize space and time because space and time are mental constructs we’ve created. Meaning, space and time don’t actually exist as an independent reality from us. It is the sheer fact that we are a continuous observer, connecting one moment to the next with memory and physical laws, that creates the concepts of space and time. It is impossible to understand or conceptualize nature or reality because then we would no longer be observers and we would become the very nature that we are trying to understand. We apply our own constructs of reality to what we observe and when we do this, we inevitably find what we call paradoxes. Basically our cognitive limitations put speed limits on our understanding of what we observe and when they don’t make sense, they become paradoxes.
Did I just make any sense? Not sure, but I’m going to go with it.
I think that is the essence of this book and it is really well done. I was very familiar with Heisenberg before this but not so much with Kant and not at all with Borges. Along with a very readable philosophy in this book you can find some nice personal accounts of these three men and the history surrounding their days. This was an excellent and thought provoking book.
I don’t read much philosophy but I read lots, and have studied, quantum mechanics. The Rigor of Angels is a beautiful crossroads of three great thinkers, Kant, Borges and Heisenberg and their attempts to explain the inexplicable. What I mean is, when we dive down onto the quantum level and compare it to the macro level, the underpinnings of our assumptions about reality disappear. The more you study the expanse of the universe and down to the quantum level, any harmony about how reality is cobbled together makes absolutely no sense. On the quantum level, there are no “things” only probability wave forms that come into existence when we look at them. How can matter and the macro world, something to us that is tangible and immutable, be made of something that kind of is and isn’t there?
This is the paradox that has vexed many people, including Einstein and Schrodinger, ever since observations and mathematics of quantum mechanics happened. What the author does in this book is assert a central thesis: we cannot understand how to harmonize space and time because space and time are mental constructs we’ve created. Meaning, space and time don’t actually exist as an independent reality from us. It is the sheer fact that we are a continuous observer, connecting one moment to the next with memory and physical laws, that creates the concepts of space and time. It is impossible to understand or conceptualize nature or reality because then we would no longer be observers and we would become the very nature that we are trying to understand. We apply our own constructs of reality to what we observe and when we do this, we inevitably find what we call paradoxes. Basically our cognitive limitations put speed limits on our understanding of what we observe and when they don’t make sense, they become paradoxes.
Did I just make any sense? Not sure, but I’m going to go with it.
I think that is the essence of this book and it is really well done. I was very familiar with Heisenberg before this but not so much with Kant and not at all with Borges. Along with a very readable philosophy in this book you can find some nice personal accounts of these three men and the history surrounding their days. This was an excellent and thought provoking book.
February 2, 2024
This is what we read for. A romp through ideas, with Egginton aiming to come at the following 4 questions:
- Are space and time infinitely divisible, or are they composed of indivisible chunks?
- Is there something like a supreme and unconditional being, or is everything in existence conditioned and affected by something else?
- Is there a spatial or temporal edge to the universe, or does it extend infinitely with no beginning or border?
- Are we free to choose our path in life, or is our every choice determined by the physical world we live in?
He does this by tossing the philosophical hot potato back and forth among Heisenberg, Kant, and Borges. And every single chapter is top notch.
Also, as an aside, this might be one of the most lucid recountings of an overly simplified vision of Kant’s Critique of Pure Reason, at least in parts. I think that takes some form of mastery over the topic. Even Roger Scruton’s attempt at a simplified introduction to Kant’s ideas in Kant: A Very Short Introduction hits you with hurdles, but I suppose that is what happens when you zoom in. Egginton shows you that it’s really all about “the capacity to convert encounters with the particular into instances of the general”.
Thanks to Goatboy for the nod on this one.
- Are space and time infinitely divisible, or are they composed of indivisible chunks?
- Is there something like a supreme and unconditional being, or is everything in existence conditioned and affected by something else?
- Is there a spatial or temporal edge to the universe, or does it extend infinitely with no beginning or border?
- Are we free to choose our path in life, or is our every choice determined by the physical world we live in?
He does this by tossing the philosophical hot potato back and forth among Heisenberg, Kant, and Borges. And every single chapter is top notch.
Also, as an aside, this might be one of the most lucid recountings of an overly simplified vision of Kant’s Critique of Pure Reason, at least in parts. I think that takes some form of mastery over the topic. Even Roger Scruton’s attempt at a simplified introduction to Kant’s ideas in Kant: A Very Short Introduction hits you with hurdles, but I suppose that is what happens when you zoom in. Egginton shows you that it’s really all about “the capacity to convert encounters with the particular into instances of the general”.
Thanks to Goatboy for the nod on this one.
October 9, 2023
There is no preferred viewpoint for observing the world around us. When everything about the present is known, nothing about the context, relations and meaning will be known. Beatrice’s (Dante’s muse) last smile happens because she is ready to enter the perfection of God’s Grace where change can’t happen while Dante must return to the world of change. The author notes that Dante seems to get the better deal, I tend to agree. A changeless universal reality would seem static to me.
Kant breaks the mode for all philosophy. He takes truth out of the universe by making it not ‘out there’, and entwines our understanding by acknowledging that space, time, and intuition are fundamental for understanding and meaning. Heisenberg realizes that we can only know what is revealed to us at one time, that position and momentum are not simultaneously knowable.
The author relies on Jorge Borges as he tells his story. That made me start to read the Borges’ book The Total Library: Non-fiction 1922-1986. There’s a lot of pleasant overlap between these two books. At the intersection of the infinite and reality there are paradoxes, or antinomies. Dante when he turns around, he sees everything and all time because just as for us moderns we know to see the big bang all one must do is stretch out your hand since the remnants for the creation of our universe is always at hand with only a now there is no past or future.
I found this book as one of the better newer books. The author never talks down to his readers. Nietzsche, Boethius, Augustine, Plotinus (it’s almost impossible to write an intelligent book without invoking Plotinus or his Enneads), Einstein, Hugh Everett III, and a host of other familiar characters are all mentioned in this book to great effect.
Kant breaks the mode for all philosophy. He takes truth out of the universe by making it not ‘out there’, and entwines our understanding by acknowledging that space, time, and intuition are fundamental for understanding and meaning. Heisenberg realizes that we can only know what is revealed to us at one time, that position and momentum are not simultaneously knowable.
The author relies on Jorge Borges as he tells his story. That made me start to read the Borges’ book The Total Library: Non-fiction 1922-1986. There’s a lot of pleasant overlap between these two books. At the intersection of the infinite and reality there are paradoxes, or antinomies. Dante when he turns around, he sees everything and all time because just as for us moderns we know to see the big bang all one must do is stretch out your hand since the remnants for the creation of our universe is always at hand with only a now there is no past or future.
I found this book as one of the better newer books. The author never talks down to his readers. Nietzsche, Boethius, Augustine, Plotinus (it’s almost impossible to write an intelligent book without invoking Plotinus or his Enneads), Einstein, Hugh Everett III, and a host of other familiar characters are all mentioned in this book to great effect.
August 24, 2023
The Rigor of Angels is a deep-dive into some of the most intense philosophical questions through the avenues of three historical figures, the physicist Werner Heisenberg, the philosopher Immanuel Kant, and the writer Jorge Luis Borges. The core of the book is the fact that, as Kant says, space and time, which we take as facts of reality, are the conditions of the possibility of experience, rather than things-in-themselves that exist outside of us. Egginton takes the reader through various paradoxes that seem utterly unsolveable which arise from the issue of taking space and time to be universal things, or from misapplication of a kind of 'God's-eye view' of the universe. One of the great beauties of the book is seeing the way philosophical ideas return again and again in different forms, and how some of the greatest problems that Borges, Heisenberg, and Kant faced were different faces of the same issues. Egginton's writing is clear and concise through even some extraordinarily complicated topics, and his willingness to use analogy and to refresh the reader at various points is very helpful. The book is dense but I found it very rewarding.
April 3, 2024
A fantastic look at the paradoxes created out of the rise of quantum mechanics. Or perhaps it is better to say that Egginton's book illustrates the paradoxes of our concept of reality as evidenced by the developments in quantum mechanics. Thematically complex, yes. But Egginton is a wonderful writer and thus every time my head started to swim, his prose brought me back on course. That is not to say that his writing allows for us to understand everything that is being presented. That is, of course, nonsense. You will re-read passages constantly. But Egginton does allow us to keep from feeling overwhelmed. I do not recommend listening to this on audio book though, for the simple reason that you will be rewinding the tape regularly.
Other aspects to appreciate about the book are the biographies of the three men mentioned in the title. All are interesting individually and their accomplishments professionally warrant study. We also get to see the roles of other titans such as Einstein, Shrodinger, Boethius and Dante.
A passage that I think sums up the gist of the book:
"What Borges's stories, Heisenberg's discovery, and Kant's system all reveal is that the assumption underlying this fantasy, the full coincidence of knowing and being, self-destructs on closer examination. On the one hand, to measure something is to differ from it in some minimal but irreducible way, and hence the very condition of knowing anything about the world demolishes the possibility of doing so perfectly. On the other hand, full presence, being truly and completely a part of the flow, requires eradicating such difference and hence makes knowledge impossible. One can imagine knowing or one can imagine being identical with the world, but only at the cost of knowing it. Like what Heisenberg's most famous principle revealed about momentum and place, we can't have both."
I will read this again. Five stars.
Other aspects to appreciate about the book are the biographies of the three men mentioned in the title. All are interesting individually and their accomplishments professionally warrant study. We also get to see the roles of other titans such as Einstein, Shrodinger, Boethius and Dante.
A passage that I think sums up the gist of the book:
"What Borges's stories, Heisenberg's discovery, and Kant's system all reveal is that the assumption underlying this fantasy, the full coincidence of knowing and being, self-destructs on closer examination. On the one hand, to measure something is to differ from it in some minimal but irreducible way, and hence the very condition of knowing anything about the world demolishes the possibility of doing so perfectly. On the other hand, full presence, being truly and completely a part of the flow, requires eradicating such difference and hence makes knowledge impossible. One can imagine knowing or one can imagine being identical with the world, but only at the cost of knowing it. Like what Heisenberg's most famous principle revealed about momentum and place, we can't have both."
I will read this again. Five stars.
April 20, 2024
Years ago as a young college student, I was dazzled by the questions and problems of philosophy—which were introduced to me by the likes of Plato, Bertrand Russell, and Erich Fromm, among others—and I ended up falling hard for it. The Rigor of Angels is a book that takes me back to that heady, blissful, mind-expanding time.
The book sets out to examine how we perceive reality, with lessons drawn from the viewpoints of three great thinkers: the physicist Werner Heisenberg, the philosopher Immanuel Kant, and the writer Jorge Luis Borges. The fascinating discussion herein ranges from physics (general and special relativity, quantum mechanics, cosmology), to metaphysics, epistemology, free will vs. determinism, morality, aesthetics, artistic criticism, literature, and history.
It’s really quite amazing how much Egginton is able to densely pack in and tie together in a mere 300+ pages of text, and without ever drifting into abstruseness. The writing is quite lucid considering the complexity of the issues, a most impressive feat of skill.
Among the primary conclusions of the book: We cannot truly know nature, but only nature exposed to our methods of questioning. And, much of our befuddlement about our existence and the universe is due to our conflation of our observations of the workings of nature and our expectations of how we think things ought to work. Often, the twain do not meet… quantum mechanics is a perfect example.
In sum, this book is an absolute gem brimming with philosophical insight and mind-bending ideas—the best read of 2024 so far—5 resounding stars. Highest recommendation for fans of philosophy & science.
The book sets out to examine how we perceive reality, with lessons drawn from the viewpoints of three great thinkers: the physicist Werner Heisenberg, the philosopher Immanuel Kant, and the writer Jorge Luis Borges. The fascinating discussion herein ranges from physics (general and special relativity, quantum mechanics, cosmology), to metaphysics, epistemology, free will vs. determinism, morality, aesthetics, artistic criticism, literature, and history.
It’s really quite amazing how much Egginton is able to densely pack in and tie together in a mere 300+ pages of text, and without ever drifting into abstruseness. The writing is quite lucid considering the complexity of the issues, a most impressive feat of skill.
Among the primary conclusions of the book: We cannot truly know nature, but only nature exposed to our methods of questioning. And, much of our befuddlement about our existence and the universe is due to our conflation of our observations of the workings of nature and our expectations of how we think things ought to work. Often, the twain do not meet… quantum mechanics is a perfect example.
In sum, this book is an absolute gem brimming with philosophical insight and mind-bending ideas—the best read of 2024 so far—5 resounding stars. Highest recommendation for fans of philosophy & science.
February 4, 2024
This was a humbling experience to say the least. Egginton gives a poetically beautiful view from perspectives of three geniuses showing how limited human mind is in understanding the nature of reality and free will. It is not just Heisenberg’s uncertainty, Kant’s antinomies or Borges’ mind bending Alef and Labyrinths, but Rigor of Angels picks brains of great thinkers millenniums apart and proves fundamental incompleteness of our understanding. It may not be rigorous enough for the experts of field but certainly a great reminder for intellectual humility. I will revisit after reading more of Borges and other classics.
October 30, 2023
The subject of this work is intriguing, and the confluence of these three thinkers is tantalizing. It promises metaphysical riches and at times, the text delivers. However, for the most part this is unfortunately less than the sum of its parts. While Egginton keeps up a well-paced roundelay between the three authors he examines, the analysis of each is repetitive and superficial. His fundamental point is that each points to the limits of our understanding as a grounding postulate for the possibility of knowledge. The very structure of reality that binds us (space, time, sequentiality) is what allows us to make sense of the world at all, and those categories are in some sense in us rather than out there. It's that loosening of the binding between objective reality and our grasp of it that Egginton finds in each thinker and that he tries to knit up into a unified lesson in the participatory universe.
That's all well and good and basically what you'd expect to pull out of these three. But I found Egginton's telling to be frustrating. He does great at the biographical detail, but the conceptual work leads him off the path into obscurantism. Rather than a careful stepwise ascent through an argument, this text prefers to leapfrog into increasingly strident denunciations of "the view from nowhere." Egginton is quick to declare that thoughts on ultimate things must founder on the rocks of an antinomy and are therefore beyond rational analysis. There's a real "gotcha!" tone, even though it doesn't always feel like he's done his homework to really police the boundaries of the sub specie aeternitatis option.
There's a lot of talk about inverting the view of the universe, the universe being a circle whose center is everywhere, etc., etc. One could discern much passion but precious little sense in these accounts. While I get where he's coming from, the details of his approach remained quite murky. I found his explanations of quantum physics muddled, even more so than is typical, and his account of Kant's philosophy reductive. Egginton tells us repeatedly how Kant was considered an intellectual superstar in his day, but he struggles to paint a clear picture of why that was so.
Egginton's account of Borges fares a little better, perhaps because he finds more emotional hooks in the pathos of spurned lovers and frustrated professional ambitions. He really only focuses on a small selection of Borges' stories, but the descriptions of the Argentinian literary scene are vivid. I also enjoyed the parts on Heisenberg's fate as the war ended and his subsequent role in the debates over nuclear weapons.
Overall, I expected to love but merely liked this book. A clearer writer could have better limned the aporia, but Egginton left me feeling like he didn't really understand what he couldn't understand, ya know? Many superior books exist that help explain the disorienting groundlessness of modern man, poised above a quantum abyss in a universe that will always escape ultimate epistemic closure. There are excellent bits in this one but it fails to reach the exalted heights it sets as its aim.
That's all well and good and basically what you'd expect to pull out of these three. But I found Egginton's telling to be frustrating. He does great at the biographical detail, but the conceptual work leads him off the path into obscurantism. Rather than a careful stepwise ascent through an argument, this text prefers to leapfrog into increasingly strident denunciations of "the view from nowhere." Egginton is quick to declare that thoughts on ultimate things must founder on the rocks of an antinomy and are therefore beyond rational analysis. There's a real "gotcha!" tone, even though it doesn't always feel like he's done his homework to really police the boundaries of the sub specie aeternitatis option.
There's a lot of talk about inverting the view of the universe, the universe being a circle whose center is everywhere, etc., etc. One could discern much passion but precious little sense in these accounts. While I get where he's coming from, the details of his approach remained quite murky. I found his explanations of quantum physics muddled, even more so than is typical, and his account of Kant's philosophy reductive. Egginton tells us repeatedly how Kant was considered an intellectual superstar in his day, but he struggles to paint a clear picture of why that was so.
Egginton's account of Borges fares a little better, perhaps because he finds more emotional hooks in the pathos of spurned lovers and frustrated professional ambitions. He really only focuses on a small selection of Borges' stories, but the descriptions of the Argentinian literary scene are vivid. I also enjoyed the parts on Heisenberg's fate as the war ended and his subsequent role in the debates over nuclear weapons.
Overall, I expected to love but merely liked this book. A clearer writer could have better limned the aporia, but Egginton left me feeling like he didn't really understand what he couldn't understand, ya know? Many superior books exist that help explain the disorienting groundlessness of modern man, poised above a quantum abyss in a universe that will always escape ultimate epistemic closure. There are excellent bits in this one but it fails to reach the exalted heights it sets as its aim.
January 7, 2024
Imagine if you will.
Trying to write an intelligible book about either: (1) Kant, or (2) Borges, or (3) Heisenberg.
Just trying to understand, let alone write about any of those figures (and their work) alone could destroy your life.
But now, just imagine writing about all 3.
And tiring ALL of their lives and work together.
And making it seem TOTALLY natural and apparent.
Easy almost.
Well.
That’s what Eggington does here.
And I can’t EVER.
I picked this one up out of desperation.
I have been reading and writing a lot of books in my field (psychology) and writing an absolutely SOUL GRINDING dissertation.
And.
I just needed a BIG THINK book.
I needed to ZOOM OUT.
And this one NAILED it.
Absolutely brilliant.
I won’t try to summarize it here.
But suffice it to say.
It’s a really good one of these.
Very gratifying.
Very humbling.
Very perspective shifting.
It will make you believe in the power of the humanities again.
And it will 10X your reading wish list.
SMASHING!
5/5 - Stars ✨
Trying to write an intelligible book about either: (1) Kant, or (2) Borges, or (3) Heisenberg.
Just trying to understand, let alone write about any of those figures (and their work) alone could destroy your life.
But now, just imagine writing about all 3.
And tiring ALL of their lives and work together.
And making it seem TOTALLY natural and apparent.
Easy almost.
Well.
That’s what Eggington does here.
And I can’t EVER.
I picked this one up out of desperation.
I have been reading and writing a lot of books in my field (psychology) and writing an absolutely SOUL GRINDING dissertation.
And.
I just needed a BIG THINK book.
I needed to ZOOM OUT.
And this one NAILED it.
Absolutely brilliant.
I won’t try to summarize it here.
But suffice it to say.
It’s a really good one of these.
Very gratifying.
Very humbling.
Very perspective shifting.
It will make you believe in the power of the humanities again.
And it will 10X your reading wish list.
SMASHING!
5/5 - Stars ✨
January 24, 2024
I liked this a lot: the intertwining of the three main figures and their time periods and their work - it didn't feel normal to jump around in time so much and that was unsettling - in a good way. I've read so many books over the years on the quantum revolution, but this book really made me think about "reality" and free will in a new way.
March 31, 2024
An interesting and mind expanding read, and I give a thank you to some GR friends who highlighted it to me. A good time for me to read it while my wits are still capable of following the themes it raised.
Knowing it would touch on something as profound as the ‘Nature of Reality’ (whatever that might be) I, of course, approached it with preconceptions - I had strong opinions, having been involved with science and technology all my life, and been interested in the background basics and the philosophy underlying science.
Fortunately the book is well enough written, covering a wide enough ground, that I soon forgot my preconceptions and just enjoyed the ideas thrown at me, and learnt something, I think.
A core feature of the book’s structure is to compare some relevant views of three key people on how they perceived reality, Nature, the physical world about us. The three selected are a quantum physicist, Werner Heisenburg; a classical philosopher, Immanuel Kant; a literary giant, Jorge Luis Borges. The author tries to show some similarities they had in viewing the world; basically, how we’re so immersed in it, such that we can’t easily define a separate reality from our perception of it.
He did a pretty good job using that approach as it’s the core of Heisenberg’s quantum mechanics, and consciously so for Heisenburg who had an interest in the meaning of his work and had familiarity with Kant. His jousts with Einstein, who had his more traditional views, are particularly interesting.
It’s also a key part of Kant’s philosophy, from his thoughts on how we relate to the world (“Critique of Pure Reason”).
However, I know little of Jorge Luis Borges and his output to know whether he focussed on Reality as much in his work, though the author here does fill us in on some of his life events and literary works to suggest he did. Given that Borges’s view on the nature of reality is the least discussed of the three I did wonder whether he’d been included just to give a literary balance to the science and pure philosophy components - any author of Borges’ acclaim is bound to have considered such a theme, on our relationship to reality, at some point but was it important to his outlook, as it was for the other two? I don’t know…
Aside from my suspicions about the choice of the three characters used to drive the narrative I found myself generally agreeing with the main thrust of the argument presented here. That we are so immersed in the world, how we experience it through our senses, that we frequently get onto dangerous ground when we try to view the world from some abstract outside position. We communicate by language, and we think, reason even, with those same words, which are themselves shaped by the everyday world we live in. I’m amazed at how far our primate brains and the language we’ve created has allowed us to develop models of the world, especially in the sciences and supported with mathematics, itself a more formal descriptive language we’ve also created.
Tackled head on, and a key theme in the book, are the apparent confusions or paradoxes arising from Heisenberg’s Quantum Mechanics description of the sub atomic world. In short, the author says these are paradoxes only because we insist on imposing our macro worldview, on objects far away from our everyday experience. Our language is not that effective in describing what we find. Mathematics, our more abstract language, does somewhat better and gives us excellent predictions of many processes that experiments can access. But there’s a limit to the understanding even from Mathematics’ success - I did a Physics degree in my youth, got good scores in my Quantum Mechanics course (I could manipulate the required equations effectively) but only in later decades did I realise my lack of philosophical understanding. For example, I’ve no idea what a ‘wave function’ in Schrodinger’s Equation actually is, other than the ultimate abstraction we use to describe quantum mechanical objects. I once, not so many years ago, realised I hadn’t even understood the full implications of the famous Schrodinger’s Cat example.
As the author notes, Nature happily goes its own way, behaving in the same manner when key experiments are done such as the critical ones with ‘two slits’ or entanglement/Bells Theorem, despite us often throwing our hands up in surprise at the results, or even calling them paradoxical. When this situation arises it’s valid to step back and question whether the rules we are attempting to impose on nature, even what we define as space and time in our macro world, are relevant here and the source of the problem.
I don’t think the author goes as far as ‘just accept what we come across as it is and don’t try to impose an understanding on it’, he does accept there is something objective out there, but I thought he came close once or twice. For example, in attempting to understand why the universe seems to be just right to support our conscious existence then, for me, the Multiverse option is a reasonable model, and I think distinct and preferable to an Intelligent Design option despite the author giving them an equivalent status - although I accept it does require some physical evidence else it remains an unproven theory! But with a bit more foundation than pure speculation.
I’m getting long winded but that shows how absorbing I found it. I was very interested in his discussion of Free Will, too detailed to go into here, but it maybe resolved some points for me.
Not an easy read because it makes you think! I needed to reflect on and reread some sections (reality is catching up on my synapse responses, it seems).
Recommended if you want a thought provoking view on humanity’s relationship with what we call the real world.
Also some interesting background biography on Heisenburg and Kant which I lacked, though a bit less on Borges.
Knowing it would touch on something as profound as the ‘Nature of Reality’ (whatever that might be) I, of course, approached it with preconceptions - I had strong opinions, having been involved with science and technology all my life, and been interested in the background basics and the philosophy underlying science.
Fortunately the book is well enough written, covering a wide enough ground, that I soon forgot my preconceptions and just enjoyed the ideas thrown at me, and learnt something, I think.
A core feature of the book’s structure is to compare some relevant views of three key people on how they perceived reality, Nature, the physical world about us. The three selected are a quantum physicist, Werner Heisenburg; a classical philosopher, Immanuel Kant; a literary giant, Jorge Luis Borges. The author tries to show some similarities they had in viewing the world; basically, how we’re so immersed in it, such that we can’t easily define a separate reality from our perception of it.
He did a pretty good job using that approach as it’s the core of Heisenberg’s quantum mechanics, and consciously so for Heisenburg who had an interest in the meaning of his work and had familiarity with Kant. His jousts with Einstein, who had his more traditional views, are particularly interesting.
It’s also a key part of Kant’s philosophy, from his thoughts on how we relate to the world (“Critique of Pure Reason”).
However, I know little of Jorge Luis Borges and his output to know whether he focussed on Reality as much in his work, though the author here does fill us in on some of his life events and literary works to suggest he did. Given that Borges’s view on the nature of reality is the least discussed of the three I did wonder whether he’d been included just to give a literary balance to the science and pure philosophy components - any author of Borges’ acclaim is bound to have considered such a theme, on our relationship to reality, at some point but was it important to his outlook, as it was for the other two? I don’t know…
Aside from my suspicions about the choice of the three characters used to drive the narrative I found myself generally agreeing with the main thrust of the argument presented here. That we are so immersed in the world, how we experience it through our senses, that we frequently get onto dangerous ground when we try to view the world from some abstract outside position. We communicate by language, and we think, reason even, with those same words, which are themselves shaped by the everyday world we live in. I’m amazed at how far our primate brains and the language we’ve created has allowed us to develop models of the world, especially in the sciences and supported with mathematics, itself a more formal descriptive language we’ve also created.
Tackled head on, and a key theme in the book, are the apparent confusions or paradoxes arising from Heisenberg’s Quantum Mechanics description of the sub atomic world. In short, the author says these are paradoxes only because we insist on imposing our macro worldview, on objects far away from our everyday experience. Our language is not that effective in describing what we find. Mathematics, our more abstract language, does somewhat better and gives us excellent predictions of many processes that experiments can access. But there’s a limit to the understanding even from Mathematics’ success - I did a Physics degree in my youth, got good scores in my Quantum Mechanics course (I could manipulate the required equations effectively) but only in later decades did I realise my lack of philosophical understanding. For example, I’ve no idea what a ‘wave function’ in Schrodinger’s Equation actually is, other than the ultimate abstraction we use to describe quantum mechanical objects. I once, not so many years ago, realised I hadn’t even understood the full implications of the famous Schrodinger’s Cat example.
As the author notes, Nature happily goes its own way, behaving in the same manner when key experiments are done such as the critical ones with ‘two slits’ or entanglement/Bells Theorem, despite us often throwing our hands up in surprise at the results, or even calling them paradoxical. When this situation arises it’s valid to step back and question whether the rules we are attempting to impose on nature, even what we define as space and time in our macro world, are relevant here and the source of the problem.
I don’t think the author goes as far as ‘just accept what we come across as it is and don’t try to impose an understanding on it’, he does accept there is something objective out there, but I thought he came close once or twice. For example, in attempting to understand why the universe seems to be just right to support our conscious existence then, for me, the Multiverse option is a reasonable model, and I think distinct and preferable to an Intelligent Design option despite the author giving them an equivalent status - although I accept it does require some physical evidence else it remains an unproven theory! But with a bit more foundation than pure speculation.
I’m getting long winded but that shows how absorbing I found it. I was very interested in his discussion of Free Will, too detailed to go into here, but it maybe resolved some points for me.
Not an easy read because it makes you think! I needed to reflect on and reread some sections (reality is catching up on my synapse responses, it seems).
Recommended if you want a thought provoking view on humanity’s relationship with what we call the real world.
Also some interesting background biography on Heisenburg and Kant which I lacked, though a bit less on Borges.
November 27, 2023
There are few books in the world that open your eyes and mind to radically new ways of seeing. They’ll make you question reality and confuse you but also provide turn posts from which you can start to glimpse a new rigor to the world. And your life after reading those books will never be the same as before. You will not see the world the same way again. This is one such book.
Want to read
September 1, 2023described as "challenging", uh oh. But I'm familiar, to varying degrees, with the three principles, so maybe. And I like the interplay between disciplines.
see also Gleiser's interview w author https://bigthink.com/13-8/william-egg...
see also Gleiser's interview w author https://bigthink.com/13-8/william-egg...
March 17, 2024
Do you remember when Firesign Theatre asked this timeless question: “How can you be in two places at once when you’re not anywhere at all?” Once before I quoted Firesign’s question in a Goodreads review of a book on quantum non-locality, and my head is similarly spinning now.
I have an inkling that this book by William Egginton might be one of the best books I have ever read. That may be saying a lot, but it is not saying that I understood it; far from it. This book is about what lies at the intersection of Kant’s epistemology, Heisenberg’s quantum physics, and Borges’s imagination, which is to say it’s sort of about what lies through the looking glass. As I write that, I am reminded of a passage in which Lewis Carroll’s poem Jabberwocky was appropriately quoted and that what I love most about this book, and about many books, is the feeling of vertigo I get when my mind is twisted beyond all reckoning. That could be why it may be one of the best books I’ve ever read: because it induces a very powerful vertigo.
The book concerns profound implications of quantum uncertainty and the impossibility of having a place of privileged observation within the universe, such as an "edge" of the universe or anyplace corresponding to a "center." Egginton makes a point of saying (I think), we can read Borges, or Dante, for a glimmer of truth concerning a center, “an infinitesimal point of origin of space and time that envelops all of creation,” but, when we gaze outward at the horizon, we must realize we are gazing inward all along. When we look out to find the edge of the cosmos, no matter what direction we gaze, we are looking at the center instead.
I am tempted to say, “this book is not for everyone,” and I guess it’s not, but that might imply that it is not for readers who do not understand, and that would mean it’s not for me. I loved it, and I’m going to read it again and hope to understand it better. That reminds me of the old saw that defines madness as doing the same thing over and over again and expecting a different result. So, if you’re mad like me, I highly recommend it. You’ll love it.
I have an inkling that this book by William Egginton might be one of the best books I have ever read. That may be saying a lot, but it is not saying that I understood it; far from it. This book is about what lies at the intersection of Kant’s epistemology, Heisenberg’s quantum physics, and Borges’s imagination, which is to say it’s sort of about what lies through the looking glass. As I write that, I am reminded of a passage in which Lewis Carroll’s poem Jabberwocky was appropriately quoted and that what I love most about this book, and about many books, is the feeling of vertigo I get when my mind is twisted beyond all reckoning. That could be why it may be one of the best books I’ve ever read: because it induces a very powerful vertigo.
The book concerns profound implications of quantum uncertainty and the impossibility of having a place of privileged observation within the universe, such as an "edge" of the universe or anyplace corresponding to a "center." Egginton makes a point of saying (I think), we can read Borges, or Dante, for a glimmer of truth concerning a center, “an infinitesimal point of origin of space and time that envelops all of creation,” but, when we gaze outward at the horizon, we must realize we are gazing inward all along. When we look out to find the edge of the cosmos, no matter what direction we gaze, we are looking at the center instead.
I am tempted to say, “this book is not for everyone,” and I guess it’s not, but that might imply that it is not for readers who do not understand, and that would mean it’s not for me. I loved it, and I’m going to read it again and hope to understand it better. That reminds me of the old saw that defines madness as doing the same thing over and over again and expecting a different result. So, if you’re mad like me, I highly recommend it. You’ll love it.
November 18, 2023
Absorbing and thought-provoking. I did not understand some large parts of it, but the writing was very beautiful. Amazing that a humanities professor could write so interestingly about quantum mechanics (and I assume accurately, given the positive blurbs from respectable physicists). I learned a lot about Borges, Kant, and Heisenberg and it was truly astonishing the intellectual linkages that could be demonstrated among them.
March 17, 2024
A mind-expanding look into some of the deepest questions regarding free will, the nature of space and time, and our limitations as observers stuck inside those constructs. Discussions on these topics are interwoven with relevant stories and anecdotes from the lives of Kant, Borges, and Heisenberg, and by the book's end I was convinced that their philosophies had more in common with each other than different. The book could get a bit pompous in the writing sometimes but was otherwise an excellent and interesting read.
October 8, 2023
Duchamp helped me see how reality is a construct and buddhism helped me see the reality of not knowing. So when a book reviewer on a podcast started to talk about how this book challenges our concept of reality via Borges, Heisenberg and Kant and how it was making her question her beliefs, i bought it right away.
What makes ‘Rigor of Angels’ powerful is taking core beliefs from literature and philosophy to buttress physics that has been around for one hundred years. However, people like me hear terms like quantum mechanics and the theory of relativity, and assume it is beyond our comprehension. However, once it is brought into the humanities, it perks my interest and makes me think I might be able to grasp it. Also, Duchamp gave me a way into concepts that before I never thought I could understand.
The gist of the books’ argument isn’t that difficult to grasp even if it goes against common sense. Space and time are constructs that allow us to observe the workings of the universe. We are unreliable observers with a limit toolset and our experience of time and space help us organize our reality but our understanding of space and time can’t be confidently extrapolated out to how the universe actually operates. It unlikely as humans in the universe we will ever be able to know how the universe works because we are inside the thing we need to observe. At best we maybe able to get more accurate in our observations but that shouldn’t be confused an actual understanding of the universe.
In a sense this is good news because we have been limited by our distaste for contradictions when in fact we need to more fully embrace and celebrate them because they often aren’t resolvable. If we accept contradictions, we accept that we live in unsettled unknowns. This humility might be a better starting point for navigating reality than what we as human beings currently use to make sense of our world.
What makes ‘Rigor of Angels’ powerful is taking core beliefs from literature and philosophy to buttress physics that has been around for one hundred years. However, people like me hear terms like quantum mechanics and the theory of relativity, and assume it is beyond our comprehension. However, once it is brought into the humanities, it perks my interest and makes me think I might be able to grasp it. Also, Duchamp gave me a way into concepts that before I never thought I could understand.
The gist of the books’ argument isn’t that difficult to grasp even if it goes against common sense. Space and time are constructs that allow us to observe the workings of the universe. We are unreliable observers with a limit toolset and our experience of time and space help us organize our reality but our understanding of space and time can’t be confidently extrapolated out to how the universe actually operates. It unlikely as humans in the universe we will ever be able to know how the universe works because we are inside the thing we need to observe. At best we maybe able to get more accurate in our observations but that shouldn’t be confused an actual understanding of the universe.
In a sense this is good news because we have been limited by our distaste for contradictions when in fact we need to more fully embrace and celebrate them because they often aren’t resolvable. If we accept contradictions, we accept that we live in unsettled unknowns. This humility might be a better starting point for navigating reality than what we as human beings currently use to make sense of our world.
November 28, 2023
Egginton tries to provide accessible explanations of both Kantian epistemology and quantum mechanics in the same book. That’s a strange and ridiculously daunting task, but the guy does a pretty good job of it by using Borges to weave Heisenberg and Kant together. All three essentially argue that certain metaphysical prejudices are central to the way we experience the world.
I loved the topics discussed, and I think he did a fine job of identifying profound connections between the three named thinkers. 18th-century philosophers influenced 20th-century physicists in some deep ways. Some mind-blowing stuff. He also provided excellent biographical background which was enjoyable to read.
If you have a doctorate on Kant or QM, you’ll obviously find some of the explanations shallow, and the structure of the book occasionally seemed repetitive or disorganized. But Egginton’s theses hold, and since this book fills such a great interdisciplinary niche, it still merits a high rating.
Hopefully I’ll get around to self-studying both classical and quantum physics at some point—but I’ll definitely be reading Borges in the interim.
I loved the topics discussed, and I think he did a fine job of identifying profound connections between the three named thinkers. 18th-century philosophers influenced 20th-century physicists in some deep ways. Some mind-blowing stuff. He also provided excellent biographical background which was enjoyable to read.
If you have a doctorate on Kant or QM, you’ll obviously find some of the explanations shallow, and the structure of the book occasionally seemed repetitive or disorganized. But Egginton’s theses hold, and since this book fills such a great interdisciplinary niche, it still merits a high rating.
Hopefully I’ll get around to self-studying both classical and quantum physics at some point—but I’ll definitely be reading Borges in the interim.
February 5, 2024
Rigor of Angels is among the best books I have ever read. Its strengths are many.
First, the subject of the book is the nature of reality, which just might be the most difficult and most interesting topic possible.
Second, the author is very clear about his main point - reality is not "out there." Since we live and perceive the world in time and space, we participate in creating reality. If there was a reality "out there" that could be perceived from following the mechanical cause-effect chain back to the first cause, then it would be a perception outside of time and space.
Third, the author, Egginton, explains and supports view of the nature of reality through the lens of literature (Jorge Luis Borges), philosophy (Immanuel Kant), and quantum mechanics (Werner Heisenberg). These three views are presented with a very clear reading of their writing.s as well as their private lives.
Fourth, exploring the nature through literature, philosophy, physics, and the personal lives of 3 significant people opened my eyes to the power of a multi-genre and multi-dimensional discussion of a topic.
I will be thinking about the ideas in this book for a long time.
First, the subject of the book is the nature of reality, which just might be the most difficult and most interesting topic possible.
Second, the author is very clear about his main point - reality is not "out there." Since we live and perceive the world in time and space, we participate in creating reality. If there was a reality "out there" that could be perceived from following the mechanical cause-effect chain back to the first cause, then it would be a perception outside of time and space.
Third, the author, Egginton, explains and supports view of the nature of reality through the lens of literature (Jorge Luis Borges), philosophy (Immanuel Kant), and quantum mechanics (Werner Heisenberg). These three views are presented with a very clear reading of their writing.s as well as their private lives.
Fourth, exploring the nature through literature, philosophy, physics, and the personal lives of 3 significant people opened my eyes to the power of a multi-genre and multi-dimensional discussion of a topic.
I will be thinking about the ideas in this book for a long time.
November 4, 2023
The world as it is is different than the world as we see it and our mental representations of it. Magritte’s “Ceci n’est pas une pipe” sprang to mind a few times while reading this, but the physics and philosophy in the book runs a bit deeper. Trying to reconcile the reality with our view of it, and whether we can ever really know it, will ultimately lead to paradox. The paradox though is a construct of our perception, not a paradox in the world. Part of what makes the book interesting is the biographical material on Borges, Kant and Heisenberg and the manner in which they came to similar conclusions through the different avenues of literature, philosophy and science. Among other paradoxes, the author makes a good run at reconciling determinism and free will and that both can exist. A thought provoking read.
March 28, 2024
An insane book, which I want to reread immediately. Although confusing at times, Egginton does a remarkable job of explaining complex ideas in physics, philosophy and literature, and somehow braiding them together into a cohesive structure.
The fundamental insight seems to be that space and time are not fundamental to reality. Instead, space and time are constructs invented by us to make sense of our lived experience, which is through observations. Observations necessarily link two moments in space-time as they are relative to the observer and the observed. Paradoxes arise when we mistakingly project aspects of our reality onto reality itself. As Heisenberg put it: "We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.”
This book explores both the consequences of this, particularly for free will, and the many paradoxes that arise if we fail to accept this position. It serves as not just a reminder of the need for epistemic humility, but a celebration of the beauty of our human limitations.
The fundamental insight seems to be that space and time are not fundamental to reality. Instead, space and time are constructs invented by us to make sense of our lived experience, which is through observations. Observations necessarily link two moments in space-time as they are relative to the observer and the observed. Paradoxes arise when we mistakingly project aspects of our reality onto reality itself. As Heisenberg put it: "We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.”
This book explores both the consequences of this, particularly for free will, and the many paradoxes that arise if we fail to accept this position. It serves as not just a reminder of the need for epistemic humility, but a celebration of the beauty of our human limitations.
January 26, 2024
A perfect sort of nonfiction book for me: trading factual narration with probing, meditative discussion; neither textbook-dry nor self-help-weaponized, but a story of people, history, and science, with a point of view and something to say, finding themes and motifs that thread it all together.
It lost me a little bit in the end with its discussion of free will, and I never got a firm handle on its description of the uncertainty principles and quantum entanglement, despite the repeated dwelling on both. Perhaps I just need to re-read it, slower.
It lost me a little bit in the end with its discussion of free will, and I never got a firm handle on its description of the uncertainty principles and quantum entanglement, despite the repeated dwelling on both. Perhaps I just need to re-read it, slower.
January 16, 2024
Very interesting and understandable even for someone who has never been comfortable with physics. Wow, what a ride. I finally feel like I understand the basics of quantum mechanics! And it was never boring! In fact, I couldn’t put it down. Highly recommended.
October 26, 2023
Given one book a year is worth saving,
this is the panacea for my craving.
this is the panacea for my craving.
February 28, 2024
I never do this but RTC, I'll also be putting the review on my substack.
Read
January 23, 2024tbh I'm too stupid to give this one a rating. Like are arguments he makes based on difficult concepts in quantum physics sound? It's so far outside my knowledge that I'm really unsure.
December 24, 2023
“Enchanted by its rigour, humanity forgets over and again that it is a rigour of chess masters, not of angels.”
― Jorge Luis Borges, "Tlön, Uqbar, Orbis Tertius"
I must admit that I'm struggling with evaluating William Egginton's "The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality". On the one hand, if I were to judge it by what it stirred in me, it would get full marks. On the other hand, I find many of its arguments unconvincing, which may not entirely be Egginton's fault in itself, but it also seems to me that the positions the author takes are often self-contradictory or argued in an obfuscated manner. Where one would like to find clarity and economy of expression, one often finds instead vagueness and verbosity.
First, I greatly appreciate ambitious works that are broad in scope, and attempt to tie together seemingly disparate ideas and characters, creating or revealing new threads. Egginton's book succeeds in this quite well. In parallel with Egginton, I have been reading Hofstadter's "Gödel, Escher, Bach" and Kandel's "The Age of Insight" which are similarly wide-ranging but they differ in one aspect that I think is quite crucial. In what I see as a contrast to Hofstadter and Kandel, Egginton seems to have much stronger pre-commitments to a particular set of philosophical positions, and then uses his main characters - Borges, Heisenberg, and Kant - to illustrate these positions in an overly monolithic and tidy way. In doing so, he seems to set up an unfortunate Procrustean bed, stretching the unlucky trio, or chopping off bits of them, to fit his arguments. People are messy, ideas are messy, and our world is messy; while this book pays lip service to the messiness of the human condition, in the delivery of its core arguments everything is tidied up with exceeding confidence.
In the last part of the book, where one would expect the culmination of the threads being woven, the reader gets an apologetic for libertarian free will, which I found to be particularly poorly argued. However, I acknowledge that I, like many people, have strong convictions on this point, and that what I perceive as weak arguments may reflect my own beliefs. Nevertheless, I found it difficult to even understand what Egginton's exact argument here was, and I couldn't shake the feeling that much of it was close to being empty sophistry. So, I will not dwell on this much, as I want to focus on what I consider to be the main idea of the book, with which the preceding parts of the book are concerned with, namely dealing with uncertainty of knowledge.
The main clash of ideas can be briefly summarized by a quote from Einstein, and a quote from Heisenberg. When confronted with the seemingly irreducible uncertainties involved in quantum mechanics, Einstein protested by claiming that "God does not throw dice", suggesting that while a process may seem uncertain to us (epistemologically), it may still be fully determined by natural laws (ontologically). In contrast, Heisenberg (and the Copenhagen interpretation), motivated by the uncertainty principle, rejects this view of hidden determination, and places uncertainty and the role of observation at the center: "We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.". In the book, Egginton strongly sides with Heisenberg and the Copenhagen interpretation, portraying Einstein as a laggard who was too set in his ways. Moreover, Egginton tries to add legitimacy to his position by claiming that the uncertainty principle is the embodiment of epistemic humility: we must humbly accept that some things are simply unknowable. And here lies the self-contradictory irony at the heart of the book's argument. While Egginton accepts uncertainty at the base level (i.e., the uncertainty of observations and knowledge), he fails to accept this uncertainty at the meta-level. He presents the Copenhagen interpretation and the uncertainty principle as the last word, without leaving any uncertainty about whether these theories themselves are wrong. For example, I think that E. T. Jaynes' Mind Projection Fallacy argument presents a solid challenge to this interpretation: it points out that it is unjustified to project the properties of our mind (e.g. ignorance) onto nature (e.g. randomness). It seems to me a more epistemically humble position to acknowledge that while it seems that Nature does play dice, it may in the future again seem that it doesn't, or (more likely) we may never know with certainty. Work in the foundations of physics is still ongoing, and there is no universal agreement on the Copenhagen interpretation - and even if there were, truth is not determined by democracy. Many times in history people have been convinced either that we know something, or that it is fundamentally unknowable, only to be proven mistaken by posterity.
In essence, Egginton disregards what the statistician Dennis Lindley has called the "Cromwell's rule", after the quote from Oliver Cromwell: "I beseech you, in the bowels of Christ, think it possible that you may be mistaken." Cromwell's rule compels us not to be completely certain of the truth or falsity of any proposition, otherwise no amount of evidence can ever change our beliefs. And it is precisely with this internal contradiction that the book stirred up again something in me that's been percolating for a while, and why I am glad to have read it. Although the metaphor may be odious (given the history of book burning), the main subjective value of some books is that they serve as kindling to light something in your mind.
Here - as is my habit - I plunge into some ill-advised, half-baked speculation: caveat emptor. It seems to me that Cromwell's rule may be exactly that fundamental principle that ought to guide our reasoning. In an attempt to axiomatize (Bayesian) probabilistic reasoning, Dennis Lindley proposed to add Cromwell's rule as an axiom to the usual axioms of probability theory. In particular, a weak version of it, that allows the propositions of formal logic to be regarded with certainty. However, one can strengthen Cromwell's rule, such that no proposition - not even of formal logic - is considered certain. This, I think, more fully embodies the spirit of epistemic humility and skepticism (and can perhaps be seen as a continuation of the skepticism of Descartes and Hume). In a further leap that strains credulity, one may ask what if we took this Cromwell's rule and probabilistic reasoning as the foundation of the whole edifice of mathematics, instead of the usual foundations of logic and set theory? It seems absurd to give up the simplicity of being able to simply state "1+1=2" without any doubt, or being able to - again, without any doubt - prove or disprove mathematical statements generally. However, perhaps there are domains where it is worth paying this price to be able to then more naturally describe, reason about, and perform computations about the phenomena in question. Many of the domains that still vex us today - forecasting and controlling complex systems, building intelligent machines that reason and act under uncertainty, quantum computing, etc. - have precisely this probabilistic character. However, there is perhaps a catch in this. What if we apply the strong Cromwell's rule to itself - if we allow ourselves to doubt the imperative of doubting everything? This could lead to some thorny paradoxes, akin to Russell's paradox, and ultimately perhaps to some interesting results similar to those of Gödel's incompleteness theorems.
Although I'd have more speculations to throw into this questionable stew, I will stop myself here, with the hope of expanding on this in some future piece of writing. (I'm borrowing a sly trick from Fermat here, without any of his aptitude.) I'm already questioning why I'm polluting the review with some very tenuously related thoughts. Maybe it is just the need to chop down a tree in this immense online forest, and hear it fall; to know that it made a sound, even if only for me. Or perhaps the irrational hope that, if someone (or something) with actual required mathematical expertise ever succeeds in rebuilding mathematics on quicksand, they will look back into the archives of the Internet and find a clumsy sketch of that endeavor in this misplaced idea, in a random book review, on a buggy (by then, probably defunct) website. That would be a joke to my (smug) taste, although by then I might not be around to enjoy the laugh.
― Jorge Luis Borges, "Tlön, Uqbar, Orbis Tertius"
I must admit that I'm struggling with evaluating William Egginton's "The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality". On the one hand, if I were to judge it by what it stirred in me, it would get full marks. On the other hand, I find many of its arguments unconvincing, which may not entirely be Egginton's fault in itself, but it also seems to me that the positions the author takes are often self-contradictory or argued in an obfuscated manner. Where one would like to find clarity and economy of expression, one often finds instead vagueness and verbosity.
First, I greatly appreciate ambitious works that are broad in scope, and attempt to tie together seemingly disparate ideas and characters, creating or revealing new threads. Egginton's book succeeds in this quite well. In parallel with Egginton, I have been reading Hofstadter's "Gödel, Escher, Bach" and Kandel's "The Age of Insight" which are similarly wide-ranging but they differ in one aspect that I think is quite crucial. In what I see as a contrast to Hofstadter and Kandel, Egginton seems to have much stronger pre-commitments to a particular set of philosophical positions, and then uses his main characters - Borges, Heisenberg, and Kant - to illustrate these positions in an overly monolithic and tidy way. In doing so, he seems to set up an unfortunate Procrustean bed, stretching the unlucky trio, or chopping off bits of them, to fit his arguments. People are messy, ideas are messy, and our world is messy; while this book pays lip service to the messiness of the human condition, in the delivery of its core arguments everything is tidied up with exceeding confidence.
In the last part of the book, where one would expect the culmination of the threads being woven, the reader gets an apologetic for libertarian free will, which I found to be particularly poorly argued. However, I acknowledge that I, like many people, have strong convictions on this point, and that what I perceive as weak arguments may reflect my own beliefs. Nevertheless, I found it difficult to even understand what Egginton's exact argument here was, and I couldn't shake the feeling that much of it was close to being empty sophistry. So, I will not dwell on this much, as I want to focus on what I consider to be the main idea of the book, with which the preceding parts of the book are concerned with, namely dealing with uncertainty of knowledge.
The main clash of ideas can be briefly summarized by a quote from Einstein, and a quote from Heisenberg. When confronted with the seemingly irreducible uncertainties involved in quantum mechanics, Einstein protested by claiming that "God does not throw dice", suggesting that while a process may seem uncertain to us (epistemologically), it may still be fully determined by natural laws (ontologically). In contrast, Heisenberg (and the Copenhagen interpretation), motivated by the uncertainty principle, rejects this view of hidden determination, and places uncertainty and the role of observation at the center: "We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.". In the book, Egginton strongly sides with Heisenberg and the Copenhagen interpretation, portraying Einstein as a laggard who was too set in his ways. Moreover, Egginton tries to add legitimacy to his position by claiming that the uncertainty principle is the embodiment of epistemic humility: we must humbly accept that some things are simply unknowable. And here lies the self-contradictory irony at the heart of the book's argument. While Egginton accepts uncertainty at the base level (i.e., the uncertainty of observations and knowledge), he fails to accept this uncertainty at the meta-level. He presents the Copenhagen interpretation and the uncertainty principle as the last word, without leaving any uncertainty about whether these theories themselves are wrong. For example, I think that E. T. Jaynes' Mind Projection Fallacy argument presents a solid challenge to this interpretation: it points out that it is unjustified to project the properties of our mind (e.g. ignorance) onto nature (e.g. randomness). It seems to me a more epistemically humble position to acknowledge that while it seems that Nature does play dice, it may in the future again seem that it doesn't, or (more likely) we may never know with certainty. Work in the foundations of physics is still ongoing, and there is no universal agreement on the Copenhagen interpretation - and even if there were, truth is not determined by democracy. Many times in history people have been convinced either that we know something, or that it is fundamentally unknowable, only to be proven mistaken by posterity.
In essence, Egginton disregards what the statistician Dennis Lindley has called the "Cromwell's rule", after the quote from Oliver Cromwell: "I beseech you, in the bowels of Christ, think it possible that you may be mistaken." Cromwell's rule compels us not to be completely certain of the truth or falsity of any proposition, otherwise no amount of evidence can ever change our beliefs. And it is precisely with this internal contradiction that the book stirred up again something in me that's been percolating for a while, and why I am glad to have read it. Although the metaphor may be odious (given the history of book burning), the main subjective value of some books is that they serve as kindling to light something in your mind.
Here - as is my habit - I plunge into some ill-advised, half-baked speculation: caveat emptor. It seems to me that Cromwell's rule may be exactly that fundamental principle that ought to guide our reasoning. In an attempt to axiomatize (Bayesian) probabilistic reasoning, Dennis Lindley proposed to add Cromwell's rule as an axiom to the usual axioms of probability theory. In particular, a weak version of it, that allows the propositions of formal logic to be regarded with certainty. However, one can strengthen Cromwell's rule, such that no proposition - not even of formal logic - is considered certain. This, I think, more fully embodies the spirit of epistemic humility and skepticism (and can perhaps be seen as a continuation of the skepticism of Descartes and Hume). In a further leap that strains credulity, one may ask what if we took this Cromwell's rule and probabilistic reasoning as the foundation of the whole edifice of mathematics, instead of the usual foundations of logic and set theory? It seems absurd to give up the simplicity of being able to simply state "1+1=2" without any doubt, or being able to - again, without any doubt - prove or disprove mathematical statements generally. However, perhaps there are domains where it is worth paying this price to be able to then more naturally describe, reason about, and perform computations about the phenomena in question. Many of the domains that still vex us today - forecasting and controlling complex systems, building intelligent machines that reason and act under uncertainty, quantum computing, etc. - have precisely this probabilistic character. However, there is perhaps a catch in this. What if we apply the strong Cromwell's rule to itself - if we allow ourselves to doubt the imperative of doubting everything? This could lead to some thorny paradoxes, akin to Russell's paradox, and ultimately perhaps to some interesting results similar to those of Gödel's incompleteness theorems.
Although I'd have more speculations to throw into this questionable stew, I will stop myself here, with the hope of expanding on this in some future piece of writing. (I'm borrowing a sly trick from Fermat here, without any of his aptitude.) I'm already questioning why I'm polluting the review with some very tenuously related thoughts. Maybe it is just the need to chop down a tree in this immense online forest, and hear it fall; to know that it made a sound, even if only for me. Or perhaps the irrational hope that, if someone (or something) with actual required mathematical expertise ever succeeds in rebuilding mathematics on quicksand, they will look back into the archives of the Internet and find a clumsy sketch of that endeavor in this misplaced idea, in a random book review, on a buggy (by then, probably defunct) website. That would be a joke to my (smug) taste, although by then I might not be around to enjoy the laugh.
October 28, 2023
The Rigor of Angels by William Egginton presents a single inescapable conclusion from three of humanity’s greatest minds: everything we know is uncertain.
Argentinian poet Jorge Luis Borges challenged the very idea of the universe, saying, “There is no universe in the organic unifying sense of that ambitious word.”
The late 18th Century German philosopher Immanuel Kant came to a similar conclusion, declaring that, “space and time are forms of intuition.”
Known as the father of quantum mechanics, Werner Heisenberg originated Uncertainty Principle. Though his arguments over particle theory with Einstein led him to the theory, it took a decade for Heisenberg to convince him that a particle’s place and its speed (momentum) cannot be measured at the same time.
Distilled to its essence, Heisenberg’s uncertainty principle proved that what we see, measure or calculate in the universe is always shaded by our participation in the process. Two centuries earlier, Kant postulated the same idea, that what we see is “our picture of the world” not the world as it exists.
“What we observe is not nature itself but nature exposed to our method of questioning.” Thankfully, Egginton arrives frequently at these clear, incisive statements because many of the concepts he discusses are truly mind-boggling.
As I worked through The Rigor of Angels, urging on brain cells in my cerebrum that had gotten lazy, the always-lively, emotionally-centered parts of my brain kept distracting me. They were asking, ‘what does this mean for my life, the way I live and the hopefulness that drives me forward?’
If we cannot be sure of anything, what is the point?
Luis Borges’ story The Aleph (1945) described a point in space that contains all other points. Anyone who gazes into it can see everything in the universe from every angle simultaneously, without distortion, overlapping, or confusion. As difficult as that is to imagine, it describes how far human understanding is away from this god-like knowledge of the universe.
Not only are we barred from knowing the universe, we’re not even capable of knowing ‘now’. Even as you say the word out loud, its echoes into the past. Quantum physicists say this in another way, that we cannot perceive a particle in a singular moment of time-space.
Fixed points of our lives – memories – are necessary to observe change (time). This means, as Kant described it, that being caught up in time, we can only look for “the elusive markers on the shore of the river of life.”
Centuries ahead of particle theory, Kant went back to Greek philosophers like Zeno (490-430 BC) to dig deeper into the concept of change. The instant before a creature moves, it is still. Ergo, he reasoned, there must be an instant when it is both still and moving.
Heisenberg’s colleague, Erwin Schrödinger presented this same conundrum as the cat in the box, a thought experiment he used on Einstein to show that contradictory ideas can both be true. In theory, the cat can be both dead and not dead.
Known as antinomies, these contradictory truths are precisely what Immanuel Kant, Jorge Luis Borges and Werner Heisenberg were each grappling with in their own way. In his early years in Argentina, Borges began thinking about how we store knowledge and use it. He came upon a contraction in the form of a man with a perfect memory.
Ireneo Funes could recall every detail of every single day he was alive. If asked to recount a given day, he could spend an entire day recalling every word said, every movement of everyone he encounters, as well as the direction of the breeze and the smells that it brought with it. Yet Funes had great difficulty functioning in the world. Because his memory was so crystal clear, he was unable to see change. Every time he walked past a mirror his own reflection startled him.
As Borges said, “Funes remembers not only every leaf of every tree in every patch of forest, but every time he perceived or imagined that leaf.” His intense memories were so overlaid that they interfered with his ability to see the present, or operate in it.
Funes stands as a counter-example to how we live. For most of us, “memory concatenates a series of impressions that evoke one another.” We utilize those imperfect impressions to inform of us of what we’re doing in the present, but if we were to lose ourselves in the precise details of the past, we’d become as dysfunctional as Funes.
“The more precisely you relive the past, the less it is a past you remember, and the more it becomes the present, vanishing before your eyes as the present always does.”
Quantum physicists confront this contradiction in the form of entangled particles. When two particles, such as a pair of photons or electrons, become entangled, they remain connected even when separated by vast distances. But Heisenberg proved two things:
1) These particles have no momentum or position until they are observed.
2) Even when entangled particles are separated by vast space, observation of one instantaneously determines the outcome of any observation of the second.
Scientists today still struggle to explain this phenomena:
The point is that we are incapable of objective observation. Even the universe will not let us examine it independently, without interfering with it. As Borges point out, we are incapable of achieving the state of The Aleph – “to see everything in the universe from every angle simultaneously, without distortion, overlapping, or confusion.”
So, what does our uncertain knowledge of the world have to do with how we live? We human do not like uncertainty. We want facts. We want to believe that we understand. But the lens through which we look at the world might as well be a kaleidoscope. We’ve trained our eyes to interpret what we see but if we don’t account for the distortion of our view, we are not seeing anything close to the truth. We must remain skeptical of what we think we see.
When I look at the conflicts in the world – the Palestinian/Israeli war, the fight between climate activists and climate deniers, socialist policies vs capitalism and the virulent disconnect between Trump supporters and progressive Americans – I see people choosing sides. We’re choosing one side over the whole truth. We seem incapable of engaging in detached observation.
Everything we witness is tainted by the POV of whoever’s presenting it and then skewed again by our interpretation of what we hear. Some of us are better than others at separating the chaff from the wheat. But whether we’re engaging in cognitive dissonance – ignoring proven facts that conflict with our chosen POV – or looking through the lens our idealism or our religion, we function more on beliefs than reality.
Many of us peg our beliefs on science. But even in that we choose a side. We let nature inform us or we believe that our technology will save us. We cling to the science that best suits us, unwilling to be uncertain.
If only we could be confident in what we know and, at the same time, uncertain of it, uncertain enough to expand our POV.
Radically conservative people say we should contract rather than expand our awareness. They decry ‘wokeness’, insisting that we should stick with what we know. But true enlightenment, expanding our knowledge, our awareness and our empathy (wokeness), means that we also have to understand the paradoxes.
For me, the paradox is that Trump supporters and people fighting for LGBTQ+ rights, for racial equality and for climate action all believe in America and have an image of what it should be.
In thinking this through, I realize that while we’re caught up in the theater of life, always ready to take the stage to declare our version of the truth, the universe is spinning along outside that theater, oblivious to what we think we know.
Time does not exist without space. Einstein proved that light travels at a constant speed of at 300,000 kilometers/second. Approaching the speed of light, time dilates, it expands.
For decades, cosmologists have been detecting in-coming cosmic radiation in every direction they point their instruments? It’s coming at us from every point in the universe and has no definable point of origin.
Egginton says that by “Freeing our minds from our senses, we find that the universe is, indeed, turned inside out.”
My question to Egginton: “How do we free our minds from our senses?”
Argentinian poet Jorge Luis Borges challenged the very idea of the universe, saying, “There is no universe in the organic unifying sense of that ambitious word.”
The late 18th Century German philosopher Immanuel Kant came to a similar conclusion, declaring that, “space and time are forms of intuition.”
Known as the father of quantum mechanics, Werner Heisenberg originated Uncertainty Principle. Though his arguments over particle theory with Einstein led him to the theory, it took a decade for Heisenberg to convince him that a particle’s place and its speed (momentum) cannot be measured at the same time.
Distilled to its essence, Heisenberg’s uncertainty principle proved that what we see, measure or calculate in the universe is always shaded by our participation in the process. Two centuries earlier, Kant postulated the same idea, that what we see is “our picture of the world” not the world as it exists.
“What we observe is not nature itself but nature exposed to our method of questioning.” Thankfully, Egginton arrives frequently at these clear, incisive statements because many of the concepts he discusses are truly mind-boggling.
As I worked through The Rigor of Angels, urging on brain cells in my cerebrum that had gotten lazy, the always-lively, emotionally-centered parts of my brain kept distracting me. They were asking, ‘what does this mean for my life, the way I live and the hopefulness that drives me forward?’
If we cannot be sure of anything, what is the point?
Luis Borges’ story The Aleph (1945) described a point in space that contains all other points. Anyone who gazes into it can see everything in the universe from every angle simultaneously, without distortion, overlapping, or confusion. As difficult as that is to imagine, it describes how far human understanding is away from this god-like knowledge of the universe.
Not only are we barred from knowing the universe, we’re not even capable of knowing ‘now’. Even as you say the word out loud, its echoes into the past. Quantum physicists say this in another way, that we cannot perceive a particle in a singular moment of time-space.
Fixed points of our lives – memories – are necessary to observe change (time). This means, as Kant described it, that being caught up in time, we can only look for “the elusive markers on the shore of the river of life.”
Centuries ahead of particle theory, Kant went back to Greek philosophers like Zeno (490-430 BC) to dig deeper into the concept of change. The instant before a creature moves, it is still. Ergo, he reasoned, there must be an instant when it is both still and moving.
Heisenberg’s colleague, Erwin Schrödinger presented this same conundrum as the cat in the box, a thought experiment he used on Einstein to show that contradictory ideas can both be true. In theory, the cat can be both dead and not dead.
Known as antinomies, these contradictory truths are precisely what Immanuel Kant, Jorge Luis Borges and Werner Heisenberg were each grappling with in their own way. In his early years in Argentina, Borges began thinking about how we store knowledge and use it. He came upon a contraction in the form of a man with a perfect memory.
Ireneo Funes could recall every detail of every single day he was alive. If asked to recount a given day, he could spend an entire day recalling every word said, every movement of everyone he encounters, as well as the direction of the breeze and the smells that it brought with it. Yet Funes had great difficulty functioning in the world. Because his memory was so crystal clear, he was unable to see change. Every time he walked past a mirror his own reflection startled him.
As Borges said, “Funes remembers not only every leaf of every tree in every patch of forest, but every time he perceived or imagined that leaf.” His intense memories were so overlaid that they interfered with his ability to see the present, or operate in it.
Funes stands as a counter-example to how we live. For most of us, “memory concatenates a series of impressions that evoke one another.” We utilize those imperfect impressions to inform of us of what we’re doing in the present, but if we were to lose ourselves in the precise details of the past, we’d become as dysfunctional as Funes.
“The more precisely you relive the past, the less it is a past you remember, and the more it becomes the present, vanishing before your eyes as the present always does.”
Quantum physicists confront this contradiction in the form of entangled particles. When two particles, such as a pair of photons or electrons, become entangled, they remain connected even when separated by vast distances. But Heisenberg proved two things:
1) These particles have no momentum or position until they are observed.
2) Even when entangled particles are separated by vast space, observation of one instantaneously determines the outcome of any observation of the second.
Scientists today still struggle to explain this phenomena:
The point is that we are incapable of objective observation. Even the universe will not let us examine it independently, without interfering with it. As Borges point out, we are incapable of achieving the state of The Aleph – “to see everything in the universe from every angle simultaneously, without distortion, overlapping, or confusion.”
So, what does our uncertain knowledge of the world have to do with how we live? We human do not like uncertainty. We want facts. We want to believe that we understand. But the lens through which we look at the world might as well be a kaleidoscope. We’ve trained our eyes to interpret what we see but if we don’t account for the distortion of our view, we are not seeing anything close to the truth. We must remain skeptical of what we think we see.
When I look at the conflicts in the world – the Palestinian/Israeli war, the fight between climate activists and climate deniers, socialist policies vs capitalism and the virulent disconnect between Trump supporters and progressive Americans – I see people choosing sides. We’re choosing one side over the whole truth. We seem incapable of engaging in detached observation.
Everything we witness is tainted by the POV of whoever’s presenting it and then skewed again by our interpretation of what we hear. Some of us are better than others at separating the chaff from the wheat. But whether we’re engaging in cognitive dissonance – ignoring proven facts that conflict with our chosen POV – or looking through the lens our idealism or our religion, we function more on beliefs than reality.
Many of us peg our beliefs on science. But even in that we choose a side. We let nature inform us or we believe that our technology will save us. We cling to the science that best suits us, unwilling to be uncertain.
If only we could be confident in what we know and, at the same time, uncertain of it, uncertain enough to expand our POV.
Radically conservative people say we should contract rather than expand our awareness. They decry ‘wokeness’, insisting that we should stick with what we know. But true enlightenment, expanding our knowledge, our awareness and our empathy (wokeness), means that we also have to understand the paradoxes.
For me, the paradox is that Trump supporters and people fighting for LGBTQ+ rights, for racial equality and for climate action all believe in America and have an image of what it should be.
In thinking this through, I realize that while we’re caught up in the theater of life, always ready to take the stage to declare our version of the truth, the universe is spinning along outside that theater, oblivious to what we think we know.
Time does not exist without space. Einstein proved that light travels at a constant speed of at 300,000 kilometers/second. Approaching the speed of light, time dilates, it expands.
For decades, cosmologists have been detecting in-coming cosmic radiation in every direction they point their instruments? It’s coming at us from every point in the universe and has no definable point of origin.
Egginton says that by “Freeing our minds from our senses, we find that the universe is, indeed, turned inside out.”
My question to Egginton: “How do we free our minds from our senses?”
Displaying 1 - 30 of 132 reviews