What We Cannot Know: Explorations at the Edge of Knowledge Paperback – January 1, 2015

As Martin van Creveld puts it, this is a very interesting book. Especially, for the great scientific erudition of whoever writes it. Marcus du Sautoy is a popularizer and professor of mathematics at the University of Oxford, known for being the host of the BBC's documentary series "The Code", about basic concepts of the history of the use and meaning of numbers.However, turning the pages it becomes clear that Sautoy eludes or ignores a great truth, without which not only science, but everything that exists lacks explanation and meaning. What is the existence of an Immobile Prime Mover, of an Uncaused Cause, etc. And whom many of us simply call God. For without the presence of him all scientific explanation falls short.Well, as stated by Albert Einstein, a great scientist and often cited by the author. Who claimed to believe in a God who shows himself through the order and harmony of universal laws.Sautoy is an atheist, but he does not make it explicit in his text. Which is fine, you don't have to. But, it is good that the readers of him know it, in order to save us several superfluous pages, full of doubts and stares into the void.

Most of the text summaries, in popular science style, what we know, mainly in physics. It only then points at what we don't know yet, or what we cannot know in principle, due to limitations presented by chaos theory, Heisenberg principle of uncertainty, singularity, etc. On top of physics the book surveys what neuroscientists and mathematicians know (and don't know) about consciousness, the consistency of mathematics (Gödel incompleteness theorem) and infinity. The book is interesting and clear. Note: in the Kindle version the formulas are displayed in a small and faint print that cannot be enlarged. Very inconvenient.

Reading this book is like sitting down with a gifted thinker and listening to his stories about exploring the brilliant success and remaining mysteries of modern physics and logic. It is entertaining and informative even if you know the issues involved, and can be appreciated even if they are new to you.

We are gifted to understand our limits, but no more. Mathematic can show us science is not everything, but there is no other way to learn the truth. Even mathematical logic have limits at self referal and infinity.Thank you, Sautoy. I found in your book what I have long been looking for, a justification of my belief. A very nice journey to the edges of human knowledge.

Excellent reading. It is like bringing mathematics into everyday life.

well written and interesting

I enjoyed this book I borrowed my local library. It discusses leading edge of mathematics, physics and cosmos as well as neuroscience among other subjects. An example of casino dice is used throughout the book to illustrate key concepts. This is very helpful. It opens your mind to question about what we know and cannot know due to limitation of human mind. Very fascinating content. The author put lot of effort to capture the history of mathematics, physics, cosmos, biology, etc. Must read for curious minds!

'Muy simpatico...' Every quote, each literary reference contained within each 'edge' effectively outlines my own epistemological journey - very well-written!!!

Take one. There is a Paul Whitehouse character in the Fast Show, called "Brilliant Kid" who wanders round a variety of landscapes exclaiming "Everything is brilliant". Reading this book made me want to do the same thing.Take two. There is a strand of speculative fiction, of which China Mieville is a leading proponent, referred to as the "New Weird". This book suggests that they haven't even got close to emulating the actual weirdness of the universe around us.The central premise of the book is that author Marcus du Sautoy is seeking to understand the limits of what we know, to stand at the boundary of human knowledge and gaze into the abyss of what we don't know. Is it infinite, or are we close to the other side, will it be possible to understand everything?While he does indeed ponder these questions, the real meat of the book, and what makes it awe inspiring, compelling, thrilling, is his exploration of what lies on this side of the boundary, a lot of the time, only just on this side.The book is divided into seven sections, referred to by du Sautoy as "edges" (of knowledge or understanding). These are, in terms of the underlying themes:-Probability, chaos theory and fractals. Unknown outcomes from a fully defined starting position.Particle physics - can we know if there is another layer of reality below the current understanding of the fundamental building blocks of the universe.Quantum mechanics. This is, of course where things start getting seriously weird. In a quantum universe particles appear out of nothing. Combining Heisenberg's uncertainty principle with the speed of light being an absolute speed limit on the universe seems to imply that space is granular not continuous. Particles on opposite sides of the universe seem to know what each other are doing.Relativity, and can we know whether the universe is finite or infinite.More Relativity, and the nature of time.What is consciousness.Finally, and as a person with a degree in hard sums, I was waiting for this, Gödel's incompleteness theorem which basically states that either a mathematical system will contradict itself or it will contain statements which can neither be proved or disproved. Du Sautoy prepares the ground for this right at the start of the book by rehabilitating Donald Rumsfeldt's words, though not the man himself. There are indeed known unknowns etc etc. What I wasn't ready for is the thought that just as geometry has stepped beyond Euclid, so the prospect has been raised that there may be different systems of mathematics. Just wow!!The only niggle I have with what is a thrilling (and I genuinely mean that about this science book), engaging, mind massaging book is both slightly surprising and, with a little thought, entirely predictable. Du Sautoy is at his hardest to follow when he is talking about his own subject, mathematics. It is as if he finds it easier to understand the lay reader's needs when he is not on his own ground.That said, this is a book in which the author shows he is admirably meeting the requirements of his role as Siminyoni Chair for the Public Understanding of Science.

This is a most intriguing book which starts and finshes with the roll of a dice. And if he does come to any definitive conclusions, and that in itself is a delightfully debatable point, one of them is that we are far more likely to understand what is happening at the outer edges of our currently known Universe than we are to understand what is happening when the dice are rolled - and how and why. I would have given it a higher rating but for the fact that he seems to meander a bit too much for my liking towards the end of the book about God. There is a linkage to the strands of thought in the book but I am not clear that it adds an awful lot. Other than that, an excellent and worthwhile read.

I had purchased "The Island of Knowledge" by Marcelo Gleiser from Amazon in May 2016.It covers a broad ranging intellectual history of our search for knowledge and meaning.I , therefore had some trepidation while buying "What we cannot Know" by Marcus du Sautoy as it appeared that the two books will have considerable overlap and simililarity of contents.However I did go for buying it , and having now read both I find that "What we cannot know" has a different tone, approach and mode of presentation.It covers seven basic themes, each called by the author "edges", which include Chaos,fractals and Complexity, atomic and sub-atomic particles, Quantum Theory, its interpretations and implications, Relativity- Special and General Theory and Conscious.For each theme / edge the author starts from the basics- the beginnings of ideas on or leading to the theme under discussion , the current state of knowledge and the unkowns and the unkowables.In between there are anacdotes and glimpses from the personal lives of main actors.Well written highly readable and strongly recommended.

Very useful for someone who did not read this fascinating subject beyond school ; a classic that is recommended to all !!

Not for the faint-hearted. Read if you know what you are getting into.