After reading about infinity and the different types of infinities in ‘Math without Numbers’ by Milo Beckman, I decided to read a whole book about infinity. I did some search and discovered Eugenia Cheng’s book, ‘Beyond Infinity : An Expedition to the outer limits of the Mathematical Universe‘.
The book is divided into two parts. The first part explores the concept of infinity in mathematics. We get to discover how we count, how we compare two collections of objects and find out which collection has more. Then we get to explore infinite sets and discover different types of infinity. On the way Eugenia Cheng shows us different sights like Hilbert’s hotel with infinite rooms, and what happens when a chessboard is filled with rice grains, putting one grain on the first square, two grains on the second, and doubling the grains till the 64th square (the result is amazing and mind-blowing!) In the second part of the book called ‘Sights’, Cheng talks about the infinitely small and infinite dimensions and other places where infinity makes an appearance.
Eugenia Cheng’s writing is charming and warm and filled with humour. It is also clear and accessible as Eugenia Cheng makes complex ideas easy to understand with real-world examples. She likes cakes and pies and they make frequent appearances in the story while discussing infinities.
I was surprised that I’ve read about most of the ideas covered in the book, like how we compare two collections, the different types of infinities, the Hilbert hotel with infinite rooms, and filling up a chessboard with rice grains – most of them in George Gamov’s ‘One, Two, Three… Infinity‘. Just shows that I’ve been reading too many books on math. Probably need a change of scene.
I enjoyed reading Eugenia Cheng’s ‘Beyond Infinity’. Hoping to read more of her books. Have you read this book? What do you think about it?
I discovered ‘Math without Numbers‘ by Milo Beckman totally by accident. Sometimes these serendipitous discoveries turn out to be amazing and that is what happened.
At the beginning of the book, Milo Beckman asks the deceptively simple question, ‘How many shapes are there?’ And before long we are taken into a dizzying tour of different kinds of shapes and how some of them are similar though they look very different and we see the world of shapes in new ways. Then Beckman asks the question, ‘Which is the biggest number?’ He then proceeds to show us what that is, and while we are reeling from the amazement that we feel with the new things we learnt, Beckman ups the ante and asks us the question, ‘Is there a number which is bigger than this biggest number?’ The answer to that is even more surprising and amazing! Then Beckman asks the question, ‘If someone says something, can we definitely prove that this statement is either true or false?’ The obvious common sense answer to this, of course, is that a statement is either true or false. What else could it be? But Beckman shows that there is more to this than meets the eye, and what we discover at the end of this conversation is a revelation.
Beckman’s style is conversational and friendly. The whole book is like having a conversation with a friend. It is beautiful. Beckman’s breezy style and humour makes us smile. For example, this passage –
“Before you go tell your loved ones that you read a book about math and learned that a square is a circle, keep in mind: Context matters. A square is a circle, in topology. A square is most certainly not a circle in art or architecture, or in everyday conversation, or even in geometry, and if you try to ride a bike with square tires you won’t get very far.”
And this one –
“When mathematicians talk about the fourth dimension, we’re not talking about time. We’re talking about a fourth geometric dimension, just like the first three. There’s up-down, left-right, forward-back, and then, let’s say, “flim-flam.” You know, another one.”
As promised in the title, there are no numbers in the book. As Beckman is fond of saying, the only numbers which are there in the book are page numbers 😊
M Erazo is the brilliant artist who has worked on this book, and their beautiful illustrations are insightful and enrich our reading experience.
When we finish reading the book, we realize that we have been taken on a breezy, fascinating, whirlwind tour of topology, analysis, abstract algebra and Gödel’s Incompleteness theorem. All complex parts of mathematics, most of which are taught at the master’s level. We don’t realize all that, of course, while reading the book, because Beckman makes it all sound simple.
I loved ‘Math without Numbers’. It is one of the best books on mathematics and science that I’ve ever read. It brings out the magical beauty of mathematics to the general reader and it is an absolute pleasure to read. I’ll just echo what Ian Stewart has said on the book’s cover – “Everyone should read this delightful book.“
One of the chapters from the book has been excerpted in Lithub. You can find it here. Hope you enjoy reading it.
Have you read Milo Beckman’s book? What do you think about it?
‘Black Hole : How an idea abandoned by Newtonians, hated by Einstein, and gambled on by Hawking became loved‘ by Marcia Bartusiak is an interesting book on the history of black holes and how the idea evolved, and how they were finally discovered. Starts from the earliest times and ends with the discovery of gravitational waves.
For me the strength of the book was the depiction of the personalities of the scientists involved. For example, Fritz Zwicky, Walter Baade, Karl Schwarzschild, Hermann Minkowski, Chandra (Subrahmanyan Chandrasekhar), Arthur Eddington, Robert Oppenheimer, J.A.Wheeler, Lev Landau and others. One of my favourite passages in the book was about Fritz Zwicky –
“Despite Caltech’s relaxed campus atmosphere, a hallmark of the California lifestyle, Zwicky retained the authoritative air of a nineteenth-century European professor. He was an aggressive, original, and stubbornly opinionated man, the supreme scientific individualist. He regularly annoyed his physics and astronomy colleagues by studying anything he pleased (he called astronomy his “hobby”) and championing along the way some pretty wild ideas, some that waited decades to be proven true. In 1933 he was the first to propose, for example, the existence of cosmic “dark matter” (what he called in German “dunkle Materie”), today one of astronomy’s outstanding mysteries. “Zwicky was one of those people,” recalled Caltech astronomer Wallace Sargent, “who was determined to show the other guy was wrong. His favorite phrase was, ‘I’ll show those bastards,’” which he did to the fullest.”
I couldn’t stop smiling when I read that 😊
I enjoyed reading this book. Hoping to read more books by Marcia Bartusiak. Have you read this one?
I loved Marcus Chown’s collection of essays on science, ‘Infinity in the Palm of your Hand‘. So I thought I’ll read this more famous book of his, ‘The Ascent of Gravity‘.
‘The Ascent of Gravity’ describes how the force of gravity was discovered and how the scientific idea of gravity has evolved across the years. The two main scientists associated with it, Isaac Newton and Albert Einstein, are featured in depth. Other scientists who played important parts in this adventure are also described. There are detailed explanations in the book on Newton’s law of gravity, Einstein’s Relativity theory, Quantum theory, String Theory and how it has tried to unify Relativity and Quantum theories. The recent detection of gravitational waves is also covered in the book.
So, the first question that needs to be asked is : how easy and accessible is the science described? I feel that the part which covers Newton is very accessible. I think everyone can understand it. There is a part about the moon’s impact on the tides which goes on and on, which I found boring. But when the chapter shifted to the tides in Jupiter’s moons, Io and Europa, I got very excited and continued reading. So when the action moves away from earth to outer space to some distant galaxies, the same thing becomes more exciting 😊 The Einstein part of the book and the String Theory part of the book is tricky. After explaining things in detail in the Newton part, the book suddenly starts using complex words in the next two parts which some readers might find a bit too much.
I have always been puzzled by gravity and the different ways in which it has been described. I was hoping that this book will give some definitive answers, but it didn’t.
I have a question for you. I’ll give you a long description first and then the question 😊
After reading this and other books, I’ve discovered that there are three descriptions of gravity.
Gravity was defined by Newton as a force between two bodies. He also gave a nice formula for calculating it. This formula has worked well for many centuries.
At the beginning of the 20th century, Einstein decided to muddy the waters a bit (or stir the pot, if you like that analogy better). He said that gravity is actually not a force. He said that the universe is made up of a fabric. He called this fabric spacetime. And things like the earth, the moon, the sun, the stars dent that fabric, they warp and curve it. This warping of the spacetime fabric makes the earth and other planets move, the way when we place a heavy ball on a flat sheet made of rubber, it creates a dent and makes the ball move. Einstein says that this is what we experience as gravity. So according to Einstein, gravity is not a force, it is not real, but it is just geometry. Einstein showed equations to prove that his concept worked.
In modern cutting edge physics, gravity is regarded as a field (like the electromagnetic field) which is composed of particles called gravitons which are responsible for the gravitational force we feel. This is still a theoretical concept. There is no evidence that gravitons exist.
Well, these are three different descriptions of the same thing – a thing that we feel everyday. They all can’t be true, can they? 😊 Because, they are all so different! So, I did some digging and went and read parts of an actual college physics textbook. This is what it said –
“Should we attribute gravitation to the curvature of spacetime due to the presence of masses or to a force between masses? Or should we attribute it to the actions of a type of fundamental particle called a graviton as conjectured in some modern physics theories? We do not know.”
Yes, I am not joking, this is what it said – this is a quote straight from the book! It seems that even scientists have no idea! They just use the particular concept which fits their current research!
When I think about it, I wonder whether this is a case of a few blind men touching an elephant and trying to find out what it is. Maybe gravity has revealed itself in different ways and maybe it is bigger than all of this and we haven’t discovered the true essence of it yet.
Which of these three explanations do you like? Which one do you find the most convincing? Please do share.
I liked ‘The Ascent of Gravity’, but I loved Marcus Chown’s ‘Infinity in the Palm of your Hand’ more. Have you read ‘The Ascent of Gravity’? What do you think about it.
I discovered Ellen Ullman’s ‘Close to the Machine : Technophilia and its Discontents‘ a few years back. It was about how Silicon Valley looked like to a person who worked at the ground level. This was probably one of the first books to describe this. I finally got around to reading it.
In the book, Ellen Ullman describes her experiences working as a programmer in Silicon Valley. Most of the book is set in the middle and late 1990s at the dawn of the Internet era. But Ullman also goes back in time and describes her experiences in the ’80s and the ’70s, and we get a ringside view of how technology and how computer culture evolved.
If you have worked in the tech industry in any capacity, but particularly as a computer programmer (I don’t know exactly what this is called these days. From ‘computer programmer’ it became ‘software engineer’, and it used to be called derisively as ‘coder’ by non-technical people in the tech industry. These days it is probably called ‘App developer’, but I’m not sure.), you’ll be able to relate to most of the things described in the book. I could. Some parts of the book made me smile, and nod in acknowledgement, while others triggered some unpleasant memories.
My favourite chapter in the book was called ‘New, Old, and Middle Age’. It is about how software technology keeps changing rapidly and how it is hard to keep up, and at some point a person gives up. It happens to everyone, and it happened to me. I still remember the heady early days, when I sat with two of my teammates while we analyzed and debugged a program and I identified the main source of a particular nasty problem and my teammates looked at me with admiration. Years later, one of my teammates taught me a new technology and asked me to hold the fort while he was away for a day, and when a customer came up with a simple request, I couldn’t handle that. That simple thing was beyond me. I knew that day that my programming days were over, and that the technology had changed to a point where I couldn’t keep up with it, and I had become obsolete as a programmer. When I read a whole chapter about it in the book, it made me smile.
I went into the tech industry because I loved programming, and I thought I’ll be on a high all the time, because I’ll be working on computer programs all the time. But reality didn’t turn out that way. There were meetings and interruptions and phone calls and this and that, and in addition to that one had to deal with the contempt that non-technical employees had for programmers, and soon, at some point, all the romance went out of the work, and I pottered around like a zombie and tried to get through the day. Ellen Ullman talks about all this in the book when she describes how when a new project starts, everyone is enthusiastic and positive, but before long things go awry, and it all goes to hell after that.
There are many other interesting things, fascinating things that Ellen Ullman talks about in the book. I’ll let you read the book yourself and experience its pleasures.
I loved Ellen Ullman’s book. As one of the first books on this theme, it is pioneering and fascinating. I wish I had read it when I was younger.
I’ll leave you with two of my favourite excerpts from the book. Hope you like them.
First Excerpt
“I once worked on a mainframe computer system where the fan-folded listing of my COBOL program stood as high as a person. My program was sixteen years old when I inherited it. According to the library logs, ninety-six programmers had worked on it before I had. I spent a year wandering its subroutines and service modules, but there were still mysterious places I did not dare touch. There were bugs on this system no one had been able to fix for ten years. There were sections where adding a single line of code created odd and puzzling outcomes programmers call “side effects”: bugs that come not directly from the added code but from some later, known permutation further down in the process. My program was near the end of its “life cycle.” It was close to death.
Yet the system could not be thrown away. By the time a computer system becomes old, no one completely understands it. A system made out of old junky technology becomes, paradoxically, precious. It is kept running but as if in a velvet box : open it carefully, just look, don’t touch.
The preciousness of an old system is axiomatic. The longer the system has been running, the greater the number of programmers who have worked on it, the less any one person understands it. As years pass and untold numbers of programmers and analysts come and go, the system takes on a life of its own. It runs. That is its claim to existence : it does useful work. However badly, however buggy, however obsolete – it runs. And no one individual completely understands how. Its very functioning demands we stop treating it as some mechanism we’ve created like, say, a toaster, and start to recognize it as a being with a life of its own. We have little choice anyway : we no longer control it. We have two choices: respect it or kill it.
Old systems have a name. They are called “legacy systems.” In the regular world, “legacy” has an aura of beneficence, Parents leave a child a legacy : fortunate child. A brother gets into a fraternity because of his older brother’s earlier membership : a legacy admission. A gift. An enrichment. The patina of age, but good age-venerability, the passing on from generation to generation. A gift of time.
In computing, however, “legacy” is a curse. A legacy system is a lingering piece of old junk that no one has yet figured out how to throw away. It’s something to be lived with and suffered. The system is unmodifiable, full of bugs, no longer understood. We say it’s “brain dead.” Yet it lives. Yet it runs. Drain on our time and money. Vampire of our happiness. Legacy.”
Second Excerpt
“I’ve managed to stay in a perpetual state of learning only by maintaining what I think of as a posture of ignorant humility. This humility is as mandatory as arrogance. Knowing an IBM mainframe – knowing it as you would a person, with all its good qualities and deficiencies, knowledge gained in years of slow anxious probing – is no use at all when you sit down for the first time in front of a UNIX machine. It is sobering to be a senior programmer and not know how to log on.
There is only one way to deal with this humiliation : bow your head, let go of the idea that you know anything, and ask politely of this new machine, “How do you wish to be operated?” If you accept your ignorance, if you really admit to yourself that everything you know is now useless, the new machine will be good to you and tell here is how to operate me.
Once it tells you, your single days are over. You are involved again. Now you can be arrogant again. Now you must be arrogant : you must believe you can come to know this new place as well as the old – no, better. You must now dedicate yourself to that deep slow probing, that patience and frustration, the anxious intimacy of a new technical relationship. You must give yourself over wholly to this : you must believe this is your last lover.”
Have you read ‘Close to the Machine : Technophilia and its Discontents‘? What do you think about it?
I’ve wanted to read Chanda Prescod-Weinstein’s ‘The Disordered Cosmos : A Journey into Dark Matter, Spacetime and Dreams Deferred‘, ever since it came out. So I was excited to finally read it.
The book is divided into four parts. The first part, which is around one-third of the book is about physics. In this part, Chanda talks about particle physics, relativity, spacetime, dark matter, quantum physics and other related things. One of the things that I loved about this part is that Chanda highlights many women physicists and astronomers. I was very happy to see one of my favourites, Vera Rubin, mentioned in the book. Chanda also mentions Lee Smolin and I was happy when I read that because Lee Smolin wrote one of the great, controversial, and most beautiful books about physics called ‘The Trouble with Physics‘.
In the next three parts of the book, Chanda describes her experiences as a physicist from different perspectives, and the issues in the field of physics and in science. For example, some of the things that she talks about are how women scientists are discriminated against, how it is doubly hard if you are a black woman, how patriarchy still controls science, how she got raped by a senior scientist and how many victims keep quiet because of the repercussions that might arise, what it means to be a black feminist working in physics research, how the land of indigenous communities have been appropriated in the name of science and how scientists have stood against indigenous communities. On the way she takes potshots at politicians and she is an equal opportunity person because she takes potshots at people on both sides of the divide. This part of the book reads like a collection of essays on related topics, and it is thought-provoking and insightful and very relevant today.
Towards the end of the book, there is a playlist and a list of recommended books. I loved them both.
The natural question that might arise is this – how easy is the science part? Can it be understood by a normal person? My answer is this. This part of the book reads like a conversation. Imagine that you are meeting your big sister, who is a scientist, after a long time. You sit down and talk to her. She tells you about work, about science, about the politics in her workplace, about the good and bad things that happened, about the new things she discovered. Sometimes, she explains things in detail. Sometimes she just mentions them or skims over them. Sometimes you understand the whole thing. Sometimes you understand only some things. But the whole conversation is pleasurable and you love it. Well, the first part of the book is this conversation. It explains some things but it won’t explain everything. Sometimes things will go over your head. But it is very pleasurable to read.
If you want to read a book which describes the basics of all that Chanda talks about, I can recommend two. One of them is ‘A Short History of Nearly Everything‘ by Bill Bryson. It covers other sciences too in addition to physics. This is the best book on science for the general reader that I’ve read. The second book is ‘The Universe in your Hand‘ by Christophe Galfard. This is the best book on physics that I’ve ever read. Galfard has explained things in a way that every reader would understand. Galfard was Stephen Hawking’s student, and though Stephen Hawking’s book ‘A Brief History of Time’ is more famous, Galfard’s book is much better in terms of ease of understanding and knocks the ball out of the park. This is one case, where the student outshone the master.
Chanda’s prose is sharp and irreverent, and filled with humour, mostly of the dark kind. Her sharp prose and humorous sentences sometimes made me laugh and sometimes made me think. For example, these sentences –
“These rules seem abstract, but they are the basis for how intellectuals on the Asian peninsula called Europe eventually came to think about space”
“During my first two years as an MLK Fellow at MIT, I was the only Black woman who worked for the physics department in Building 37 who wasn’t a member of the janitorial staff.”
“White men who weren’t raped and don’t have to deal with racism have been more productive than me for the last three days.”
“The sun has about five billion years left before it destroys Earth, but it’s hard to imagine that our species, which has only been around for a couple million years, will last that long.”
Chanda talks about her mother many times and the sacrifices her mother made so that Chanda could get a good education and accomplish what she did, things that Chanda didn’t know when she was young, because her mother made these sacrifices quietly. One of my favourite passages about her mother was this one. It melted by heart and made me cry. Mothers are amazing. What will we do without them?
“I once asked my mother in a moment of doubt what the point of my work was, and she said that people need to know that there is a universe beyond the terrible things that happen to us. The stars, the Standard Model, the way spacetime bends—this way of seeing the world is one that can be inspiring.”
There is a note to the reader at the end of the book in which Chanda says this. I found it very inspiring.
“Science is not about what we know. Science is about what we don’t know. A scientist’s job is to live at the boundary of what is known and unknown and try to push that boundary forward. That requires being confused—and being comfortable with not knowing the answers because we are confident that we’ve got a good toolkit. Early drafts of this book emphasized this in places, but I was afraid these notes would disrupt the reader’s focus on what I admit is a lot of new and weird information about how the universe supposedly works. The key thing is that if you’re feeling confused but intrigued and wanting to learn more, you’re having a very “scientist” experience.”
Here is the part of the book in which Chanda talks about the great Vera Rubin. It is long, but I couldn’t resist sharing it, because I want everyone to read it.
“Kelvin, Poincaré, and Zwicky are all historicized as genius giants of their time, and mysteriously Vera Rubin generally hasn’t been. In Rubin’s lifetime, men younger than her won Nobel Prizes for finding evidence of phenomena that were similarly significant to finally proving the existence of something behaving like an invisible matter (the 2011 prize for dark energy)…
As a graduate student who was struggling with self-confidence and her place in the theoretical physics community, I once spent a day with Dr. Rubin. When I met her, almost the first thing she did was ask me how I thought the dark matter problem could be solved. No one had ever asked my opinion about a major problem in physics before, not in grad school, and definitely not in college. Physicists are rarely interested in the opinions of undergraduates, who are often not deemed advanced enough to make a useful contribution to the conversation. In research, the convention is that one hands an undergraduate a problem to work on and hopes they will be creative in their efforts to apply known techniques to tiny fractions of difficult problems.
In some sense, I understand this. And yet some of the most interesting research I have done as a scientist was a collaboration with undergraduates who dug in and went beyond their coursework, asking questions and finding interesting threads in the work. Importantly, physics is about precisely that, which means that we should probably be asking our undergraduates big-picture questions, not for the sake of getting solutions out of them, but to encourage them to take ownership over those questions. But what if you never give yourself permission to think about a problem? This is what happened initially between me and dark matter. I understood it as a problem for observational astrophysics, not particle theory, and as a result, I wasn’t particularly interested in it for myself. I thought it was an important problem, but not my problem. Vera Rubin changed that impression, simply by asking me the question.
What Dr. Rubin did was probably more anti-establishment than it already seems. Not only did she ask a student what she thought about how to solve one of the biggest problems in physics, she also asked me, a brown-skinned woman. I suspect that along the way some undergraduates do get asked for their opinions. I watched as a few of my white, mostly male classmates were feted as next-generation physics greats. It became clear to me early on that the faculty had decided that I was not going to be in that particular group. Why ask someone who would never amount to anything as a scientist what she thought about science? Dr. Rubin challenged how I was treated in physics by treating me as if I was a person who could solve a major problem in physics. At the time I wasn’t working on dark matter and didn’t have a good answer for her. It was another five years before I ended up in dark matter’s intellectual orbit, and even at that point, I had no intention of becoming a person who works on dark matter. A colleague suggested we try to make sense of a proposed theory about how axion Bose-Einstein condensation works. As a result of our efforts, we produced an interesting result and suddenly I found myself, Dr. Rubin’s encouragement at my back, thinking that I too could be one of the people hot on the trail of dark matter.”
I enjoyed reading ‘The Disordered Cosmos’. It was powerful, insightful and made me think a lot. It is an unusual physics book, because it doesn’t just stop with physics, but talks about people and the environment in which they work in. Chanda says towards the end of the book that she didn’t want to write a detached book about science, but she wanted to write a book which showed things as they were and how science was practised. The result is, of course, glorious.
Have you read ‘The Disordered Cosmos‘? What do you think about it?
I have heard of ‘Uncle Petros and Goldbach’s Conjecture‘ by Apostolos Doxiadis for years and I finally decided to read it. I loved the graphic non-fiction book ‘Logocomix‘ which was co-authored by Apostolos Doxiadis and so was excited to read this.
The narrator of the story is a teenager in high school. He hears stories about his eccentric Uncle Petros from his dad and his other uncle. Though they both acknowledge that Uncle Petros was brilliant, they also regard him as a failure. So our narrator decides to find out more about Uncle Petros, and while he is attempting to do that, he stumbles upon the mysterious Goldbach’s Conjecture, one of the great unsolved problems in mathematics, which Uncle Petros had attempted to solve. The rest of the story is about what happened to Uncle Petros and his quest for solving the puzzle posed by the Goldbach Conjecture.
Though this book is a novel, it offers a dazzling overview of the history of mathematics in the twentieth century, especially the foundations of mathematics and number theory. Many great 20th century mathematicians make a guest appearance in its pages, including G.H.Hardy, Srinivasa Ramanujam, Kurt Godel, Alan Turing. The mathematics in the book is descriptive and informative and enjoyable and it is never intimidating. There is no equation in the main text. One can just read the story and enjoy the information it shares, or if one is more adventurous, one can research more on the things that the book talks about. So the book can be read in many ways at multiple levels. The story told in the book is also very beautiful and inspiring.
I enjoyed reading ‘Uncle Petros and Goldbach’s Conjecture‘. It made me think of George Gamov’s Mr. Tompkin books. But while Gamov’s book focuses more on the science, I think this book perfectly balances the math and the story, while leaning more towards the story, thus making it more appealing to the general reader.
I’m sharing a couple of my favourite passages from the book below. Hope you like them.
“…real mathematics has nothing to do with applications, nor with the calculating procedures that you learn at school. It studies abstract intellectual constructs which, at least while the mathematician is occupied with them, do not in any way touch on the physical, sensible world…Mathematicians find the same enjoyment in their studies that chess players find in chess. In fact, the psychological make-up of the true mathematician is closer to that of the poet or the musical composer, in other words of someone concerned with the creation of Beauty and the search for Harmony and Perfection. He is the polar opposite of the practical man, the engineer, the politician or indeed, the businessman.”
“During the course of the lessons I witnessed an amazing metamorphosis. The mild, kindly, elderly gentleman I had known since my childhood, one easily mistaken for a retired civil servant, turned before my eyes into a man illuminated by a fierce intelligence and driven by an inner power of unfathomable depth. I’d caught small glimpses of this species of being before, during mathematical discussions with my old room-mate, Sammy Epstein, or even with Uncle Petros himself, when he sat before his chessboard. Listening to him unravel the mysteries of Number Theory, however, I experienced for the first and only time in my life the real thing. You didn’t have to know mathematics to feel it. The sparkle in his eyes and an unspoken power emanating from his whole being were testimony enough. He was the absolute thoroughbred, pure unadulterated genius. An unexpected fringe benefit was that the last remaining trace of ambivalence…regarding the wisdom of my decision to abandon mathematics was now dispelled. Watching my uncle do mathematics was enough to confirm it to the full. I was not made of the same mettle as he – this I realized now beyond the shadow of a doubt. Faced with the incarnation of what I definitely was not, I accepted at last the truth of the dictum: Mathematicus nascitur non fit. The true mathematician is born, not made. I had not been born a mathematician and it was just as well that I had given up.”
Have you read ‘Uncle Petros and Goldbach’s Conjecture‘? What do you think about it?
I have wanted to read T.H.White’s ‘The Goshawk‘ ever since I discovered that Helen MacDonald’s ‘H is for Hawk’ was inspired by it. I finally got to read it today.
Sometime in the 1930s, T.H.White quits his job as a schoolteacher, moves to the countryside, and gets a goshawk, which is a type of hawk, and tries to train it. As a guide, he uses a hawk training manual written in 1619, which is clearly outdated. He describes this experience in this book. There are two parts to the book. One part is about how White trains the hawk. The second part is the one in which he describes the personality of the hawk, his relationship to the hawk, and delves into the history of hawk training, and takes digressions into literature, like when he describes how falconry / hawk training is embedded in some of Shakespeare’s plays. The first part was filled with a deluge of details which would be of interest to a fan of falconry. I was lukewarm towards it. I loved the second part. It was beautiful. Of course, the two parts are not clearly split, but are interwoven together like the warp and weft which make a fabric. So White will be talking about how he is training his hawk and I’ll find that hard to read and will be wondering when it will end and whether I should continue reading the book, when suddenly, there will be a page on the history of falconry or on how his hawk regarded him with contempt and he couldn’t do anything about it, and I’ll smile and will continue reading.
The book had these legendary lines –
“But what on earth was the book to be about? It would be about the efforts of a second-rate philosopher who lived alone in a wood, being tired of most humans in any case, to train a person who was not human, but a bird.”
“To train a person who was not human, but a bird” – how beautiful is that?
I loved the places in which White describes how his hawk regarded him with contempt, refused to listen to him, and he couldn’t do anything about it, because you can’t tame a hawk or make the hawk listen to you by force, and only patience, kindness and gentleness will work, while the hawk continues to treat you with contempt 😊 That passage goes like this –
“I could never make up my mind whether I was the master. Gos regarded me with tolerant contempt. He had no doubts about who was the slave, the ridiculous and subservient one who stood and waited. For himself, he had the whole day to fill in.” 😊
I also loved the passages where White describes how his hawk regards his love or kindness with suspicion, because the hawk knows instinctively that humans show kindness to it because they want to conquer its will and enslave it. It was amazing to discover how much wisdom was encoded in the hawk’s wild instinct. I also loved the part where White talks about how a hawk which grows up in the wild is sleek and cool and an accomplished hunter, because it was trained by its hawk parents and then learnt more by experience, while the hawk which is trained by humans is clumsy and a poor imitation of the wild version. Of course, this leads to the natural question on why train a wild bird like a hawk, when it can do better on its own, why reduce this magnificent wild being to a human pet. Well, that is a discussion for another day.
I enjoyed reading ‘The Goshawk‘. Marie Winn says in her introduction that it is a cult book now. At the time it was published in the 1950s, it must have been a unique book. I don’t know any other mainstream writer from that time trying to train a hawk or a wild animal and writing about it. T.H.White seems to have been an interesting, fascinating person.
Have you read ‘The Goshawk‘? What do you think about it?
I read in the news today, that Steven Weinberg, one of the great physicists to walk the earth during our times, is no more. I have a soft corner for great physicists, and I felt very sad.
Steven Weinberg won the Nobel Prize for Physics in 1979 for making fundamental contributions to the Standard Model of Particle Physics. But for a science enthusiast and physics lover and book reader like me, my introduction to Steven Weinberg was through his book on the Big Bang Theory for the general reader, ‘The First Three Minutes‘. It is one of the great books written about the Big Bang Theory and the origin of the universe. How accessible is it? Can anyone understand it? That is a hard question to answer. I think it is easier than Roger Penrose’s books but harder than George Gamov’s, Simon Singh’s and Christophe Galfard’s. Weinberg himself says this in the preface of his book –
“I had better say for what reader this book is intended. I have written for one who is willing to puzzle through some detailed arguments, but who is not at home in either mathematics or physics. Although I must introduce some fairly complicated scientific ideas, no mathematics is used in the body of the book beyond arithmetic, and little or no knowledge of physics or astronomy is assumed in advance…However, this does not mean that I have tried to write an easy book. When a lawyer writes for the general public, he assumes that they do not know Law French or the Rule Against Perpetuities, but he does not think the worse of them for it, and he does not condescend to them. I want to return the compliment: I picture the reader as a smart old attorney who does not speak my language, but who expects nonetheless to hear some convincing arguments before he makes up his mind.”
I think Weinberg’s words describe the book perfectly. That is, if we put in the effort, while reading the book, we’ll be rewarded. I was.
One of the things I loved about Weinberg was the confidence he had as a scientist when he explained something, or made an analysis or prediction. But he also interwove that confidence with natural scientific scepticism and humility. The perfect combination of these two made his authorial voice pure music to listen to. For example, read this passage –
“In following this account of the first three minutes, the reader may feel that he can detect a note of scientific overconfidence. He might be right. However, I do not believe that scientific progress is always best advanced by keeping an altogether open mind. It is often necessary to forget one’s doubts and to follow the consequences of one’s assumptions wherever they may lead – the great thing is not to be free of theoretical prejudices, but to have the right theoretical prejudices. And always, the test of any theoretical preconception is in where it leads. The standard model of the early universe has scored some successes, and it provides a coherent theoretical framework for future experimental programs. This does not mean that it is true, but it does mean that it deserves to be taken seriously.”
‘The First Three Minutes‘ ends gloriously with one of the great passages that I’ve ever read in any science book, nearly elevating the book to a work of existentialist philosophy, asking all the big questions that humans have asked since the beginning of time. Here is how it goes –
“However all these problems may be resolved, and which ever cosmological model proves correct, there is not much of comfort in any of this. It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes, but that we were somehow built in from the beginning. As I write this I happen to be in an airplane at 30,000 feet, flying over Wyoming en route home from San Francisco to Boston. Below, the earth looks very soft and comfortable – fluffy clouds here and there, snow turning pink as the sun sets, roads stretching straight across the country from one town to another. It is very hard to realize that this all is just a tiny part of an overwhelmingly hostile universe. It is even harder to realize that this present universe has evolved from an unspeakably unfamiliar early condition, and faces a future extinction of endless cold or intolerable heat. The more the universe seems comprehensible, the more it also seems pointless. But if there is no solace in the fruits of our research, there is atleast some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desks for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.”
When I read the lines – “It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes” – it makes me laugh, it almost feels like dark comedy from a Coen brothers movie 😊
That last passage is one of my all-time favourite passages from any science book.
As you can tell by now, Steven Weinberg’s ‘The First Three Minutes‘ is one of my favourite books on science and physics. Did I understand it completely? Definitely not. Did I understand most of it? Yes, I did.
Steven Weinberg was one of the last great scientists from the 20th century who was around when the great exciting things happened in physics – relativity, quantum physics, particle physics. He had a front row seat when many of these great things happened, and he played an active part and contributed to some of them. Many of the great scientists who made these great advancements were well known to him or were his friends. With his passing, we have nearly reached the end of an era. My favourite Roger Penrose is still around, but I am dreading the day, when he will move on.
Steven Weinberg lived a long life, a beautiful life, extended the frontiers of his field, and enhanced our understanding of the universe. It was a privilege and an honour to be around at the same time as the great Weinberg. I am glad our times overlapped. It is sad that all beautiful things have to come to an end. It is a heartbreaking day for science lovers and physics fans.
Farewell, Professor Weinberg. Thank you for all the beautiful things you did to extend the frontiers of science. We’ll never forget you and we’ll miss you. I can only repeat what Horatio tells Hamlet when he bids him goodbye – “Farewell, sweet prince. May flights of angels sing thee to thy rest.”
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