TheInfinite BookA Short Guide to the Boundless, Timeless and Endless

by John D. Barrow

For a thousand years, infinity has proven to be a difficult and illuminating challenge for mathematicians and theologians. It certainly is the strangest idea that humans have ever thought. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Is matter infinitely divisible into ever-smaller pieces? But infinity is also the place where things happen that don't. All manner of strange paradoxes and fantasies characterize an infinite universe. If our Universe is infinite then an infinite number of exact copies of you are, at this very moment, reading an identical sentence on an identical planet somewhere else in the Universe.Now Infinity is the darling of cutting edge research, the measuring stick used by physicists, cosmologists, and mathematicians to determine the accuracy of their theories. From the paradox of Zeno’s arrow to string theory, Cambridge professor John Barrow takes us on a grand tour of this most elusive of ideas and describes with clarifying subtlety how this subject has shaped, and continues to shape, our very sense of the world in which we live. The Infinite Book is a thoroughly entertaining and completely accessible account of the biggest subject of them all–infinity.From the Trade Paperback edition.

Genres: Science, Nonfiction, Mathematics, Philosophy, Physics, Popular Science, History

Paperback

First published February 14, 2005

About the author

John D. Barrow was a professor of mathematical sciences and director of the Millennium Mathematics Project at Cambridge University and a Fellow of the Royal Society.

He was awarded the 2006 Templeton Prize for "Progress Toward Research or Discoveries about Spiritual Realities" for his "writings about the relationship between life and the universe, and the nature of human understanding [which] have created new perspectives on questions of ultimate concern to science and religion".

He was a member of a United Reformed Church, which he described as teaching "a traditional deistic picture of the universe".

Reviews

[WarpDrive · Rating 4 out of 5]

An interesting, multi-disciplinary introduction to the fascinating theme of infinity (and associated aspects such as the "infinitesimal"), as a concept explored from a mathematical, physical, philosophical, computational and ethical/sociological perspectives.

The points of discussion and analysis introduced by the author are many and some of them quite original; this book frequently generates opportunities for serious reflection, especially in relation to his philosophical approach, where I found myself agreeing strongly with many of the author's points.

The areas that let me down a little bit (but this should not be so much a reflection of shortcomings on the author's part, but rather a question of my own personal tastes and requirements), are the more technical areas devoted to mathematical analysis, the physical sciences and theory of computation, which I found a little bit too "popular" and superficial:
- as far as mathematics is concerned, the author (who, by the way, actually is a professor of mathematical sciences) does not explore in detail how axiomatic systems deal with such concept: I would have expected at least a brief analysis of controversial, fascinating and important axioms such as the Axiom of Choice, of the critical foundational role played by Zermelo's "Axiom of Infinity", and of the main arguments in favour or against the "finitistic" approach to mathematics. He also avoids important angles of approach, such as the different but related issues of continuity, differentiability class, analyticy, the fundamental concept of transfinite induction, differentiable manifolds etc. If you want to seriously explore this fascinating theme in mathematics, there are better books that address it to a more satisfactory level. On the other hand, some basic concepts such as series convergence are treated quite well, even though a more detailed treatment of convergence radii would have been helpful. The exploration of Zeno's classes of paradoxes and the explanation of a "resolution" of such paradoxes by exploring the links with special relativity are executed quite well.
- In the area of the physical sciences, he does tend towards a particular class of inflationary models (the so-called "eternal inflation"), underestimating the degree of debate and the controversial nature of this particular class of models. While there is sound experimental confirmation of the fact that some model of inflation is the most promising, the jury is still out when it comes to the selection of the actual type of inflation model which best reflects existing experimental evidence. Any form of "Multiverse" theory, in particular, is still generally regarded as highly speculative and there are a few experts in the field who are very vocal in criticizing it as an intellectual cop-out. The author spends much room analyzing the implications deriving from his favored class of inflationary models: space that might have been used instead, in my personal opinion, to address in more detail some other interesting themes, such as, for example, the relationship between the mathematical approach to infinity and the physical world: is spacetime isomorphic to the mathematical continuum ? Or, does the very concept of continuum need re-thinking at Plank scale, as it appears to be the case ? What about the Noether's theorems, which are fundamental in modern physics and which assume continuous symmetries (more appropriately: "to every differentiable symmetry generated by local actions there corresponds a conserved current") ? To what extent does the "Cantor paradise" have some correspondence to the physical world? And, stretching this point to the extreme and morphing the issue into the realm of highly speculative investigation, is it possible to envisage a feasible model of the Universe, under existing experimental evidence, with a transfinite spacetime? Are all aspects of the Universe restricted within the realm of the countably infinite ? Entire books have been written on this particular debate, so more detail here would have been highly welcomed.
- I would have also loved an analysis of the whole issue form an information theoretical perspective, which is quite lacking in this book. A real pity, as this perspective is quite important, and has increase in importance. For example, the case of Maxwell's demon has been explained well in the book, but it could have been explained at least equally well more explicitly in terms purely of the entropy cost of information processing. Information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer’s principle, is not mentioned in the book. The treatment in the book is correct, mind you: it is just that I would have liked a more formal and rigorous information theoretical approach.
In more general terms, the type of discussions like the ones raised in the famous "Feynman Lectures on Computation" would have been a great item of analysis in this book. The computational theory aspects of the concept of infinity are touched, but investigated by the author only very briefly and succinctly.

In general, however, this book has been for me a really enjoyable experience, notwithstanding the "popular" nature of its more "technical" sections (if you want to delve deeper into the more technical aspects, you'd probably be better off resorting to less introductory sources). It is a very nice, highly informative, well-written and competently developed multidisciplinary introduction to the subject, especially with regards to the philosophical analysis of this fascinating concept. I particularly enjoyed the issue of prospective immortality as a potentially poisoned chalice, even though I do not necessarily see this as a pure dichotomy between mortality and immortality: aspects of choice (the perspective of being able to freely decide WHEN to die, rather than IF) should have been investigated further, in my opinion. However I found the author's position quite interesting and agreeable, and actually a bit surprising (given the author's self-proclaimed "deistic" position, not necessarily in synch with the views expressed in his book, which I personally feel would probably lean more towards an atheistic or at least an agnostic position).

Highly recommended: 4 stars.

[Adam · Rating 5 out of 5]

As I started studying Calculus more and more it made me a lot more curious about the nature of infinity. We take these limits of functions to get the derivation process, we look at area with integration by summing infinitely small pieces under a curve, and then we look at the divergence and convergence of a series with limits to see what these things do at infinity. Then, to top it off, I had my mind further blown by discussing infinite dimensions in Linear Algebra. Needless to say, I had infinity on my mind. However, I wanted a more informal book to read to pass the time. Studying the formal texts is fun, but can get tedious.

Barrow's book "The Infinite Book" is exactly what I was looking for. Don't worry, if you're not a mathematician you can still grasp the general concepts discussed in this book. One of the great aspects of this book is that Barrow brings through a bit of the history of infinity. With that in mind you take a walk through the history of infinity and how it touches human curiosity. Natural he makes reference to Zeno's Paradox. (I'm actually getting sick of reading about this, it feels like just about every math book I read discusses Zeno. Don't get me wrong, it's definitely relevant.) Anyway, some of the more interesting stuff comes when he gets to discussing Cantor's history. I found this utterly fascinating and Cantor did some impressive work with infinity.

Naturally Barrow ups the ante as the history gets to more modern day applications. Cosmology being a major one, but he also brings us through some of the more "pop culture" elements (if I dare call them that). Such as strange movies that involve things like an infinite game, which are now movies I intend to track down and watch. Some of this material may be beyond some readers, it was a little beyond me at times, but I wouldn't say it was so overwhelming I got totally lost in what was being discussed.

If you're at all curious about the nature of infinity, then I highly recommend this book. I would even rank this as a rather exhilarating read. Barrow approaches the subject in an excellent way and not in a way where I think non-mathematicians will feel put aback by the arcane discussions. After reading this I am definitely interested in reading other books by Barrow and I would definitely recommend this to anyone interested.

[maï! · Rating 3 out of 5]

PUNAISE ENFIN TERMINÉ la lecture a été interminable

j'ai quand même bien aimé c'était vraiment super intéressant !!! le seul truc chiant c'est que j'me suis un peu forcée à le lire vu que j'avais que 3 semaines (il vient de la médiathèque) dcp ça a un peu gâché le plaisir de lecture mais c'est pas grave

j'ai appris énoooormément de choses et ça me hype trop pour les autres livres sur l'infini et l'univers que j'ai pcq y'a plein de points que j'aimerais approfondir

bon par contre on va pas se mentir qu'à certains moments j'avais absolutely no clue de ce qui était raconté PTDRRRR

[Mayank · Rating 3 out of 5]

Well, the good thing is, I managed to finish this book in a finite amount of time. At one point it looked unlikely.

Its not a bad book at all (in fact its quite good), but its a book written by a mathematician, with the assumption that mortals readily understand the meaning of words like 'topology' and 'singularity'. The only places where the book loses its grip is where the author succumbs to this trap.

Having got that out of the way, there are a number of things I liked about this book. First and foremost, it attempts to structure and explain the latest attempts by science to answer the question 'Is our universe infinite'? Of course it does'nt answer this and other large questions conclusively, but it certainly opens up new areas of thought.

I also liked the fact that the question of infinity is approached from various perspectives - namely scientific, theological, and mathematical. While some might argue that such an approach is logically inconsistent, I enjoyed the experience. There are certain parts of the book which diverge to speculative areas like time travel and immortality which I liked, but I can understand the grouse that a purist might have with this approach.

While I give the book a three star rating, this is merely a reflection of my limitations in understanding some of the heavier technical concepts the author mentions. It is the reason why parts of the book were difficult for me to get through, as I mentioned right at the start.

On the whole, reading this was an enjoyable experience, but occasionally difficult to comprehend.

[Philemon - · Rating 5 out of 5]

This book far exceeded expectations. The author uses a lucid style, but one that delves easily into complex areas. He addresses meanings and implications of infinity not only in mathematics, but also in metaphysics, and most interesting to me, cosmology. In doing the latter he clears up many concerns that have been troubling me, especially concerning the multiverse and the question of whether we're living in a simulation. The author, a Cambridge don, has written five or six other explanatory books on math and science which I plan to look into. His prose strongly conveys a commitment to explain complexities clearly to a wide lay readership, but without cutting corners. You feel he's ranging over everything he knows on the subject at hand, but somehow avoiding obfuscation or condescension.

[Antonio Fanelli · Rating 4 out of 5]

Argomento affascianante ma ostico.
Abbastanza semplice e comprensibile la scrittura.
Ci sono punti che proprio non capisco, ma complessivamente è molto ben scritto.

[Dymbula · Rating 4 out of 5]

Kdysi nám syn rozmlátil pohled na svět tím, že nám na zahradu přišel sdělit, že existují malá a velká nekonečna. Časem jsme si zvykli a dokonce to i částečně pochopili. Pak jsem si přečetl Knihu o nekonečnu. Udělala mi ve všem takový bordel, že ho budu zdlouhavě uklízet. Autor mi ukázal, že s nekonečny je to daleko složitější. Jsou prý nekonečna absolutní, matematická a fyzikální. Ta absolutní jsou celkem v pohodě, o těch se dá beztrestně žvanit z kazatelen, z kateder filosofických fakult i v hospodě nebo u ohně. Nejsou nebezpečná a může se o nich hovořit i bez patřičného vzdělání. Často není třeba ani důkazů. Pak jsou matematická nekonečna. Ani ta nejsou nebezpečná, jen je potřeba umět matematiku a myslet. Tam se schovávají i ta malá a velká nekonečna. Matematici si s nekonečny hrají s jistou elegncí a může to být i srozumitelné. Ta poslední, fyzikální, jsou podle autora nebezpečná a jsou schopna rozdrtit kdejakou teorii a zamotat vším, na co jsme v našem světě zvyklí. Z fyzikálních nekonečen jsem při čtení pociťoval neklid. A tak si říkám: "Bejt o trochu blbější, ani bych se do té knížky nepustil a měl bych pokoj." No však si ji přečtěte, ať víte, o čem se tu snažím psát.

[Benjamin Wallsten · Rating 4 out of 5]

Review taken from my blog,The Virtuosos.

Infinity. What is it? What is it not? Why should anyone care about something so intangible?

For many people. infinity is just a word that they’ve been taught means, “without bound; forever; bigger than anything; beyond comprehension.” It’s usually associated with mathematics, especially math of a “higher order,” like Calculus. And it seems intuitively familiar despite an utter lack of understanding for the most part.

Barrow takes the everyday view of infinities (because, as you’ll learn, there are different types of infinity – thank Georg Cantor for that (I’m serious)) and meticulously attempts to teach us where we’re wrong and where we’re right. He illustrates just how much we aren’t built to accurately register, mentally, the nuances of such concepts. As a passing example, what happens when you add any two numbers together? We all know that. That’s easy. You get a sum, a finite sum. One that yu can, theoretically count up to. The same rule applies to the other major mathematical operations (division, subtraction, multiplication). However, what if I asked you to add a finite number to infinity? Or subtract a finite number from infinity? Whatever the operation, the outcome will be the same: we’ll still have infinity as an answer. You may ask if that infinity is the “same size” as the original infinite, and guess what, it is. If you double infinity you still have infinity, and both infinities are the “same size!”

Needless to say, common sense is not really our friend when it comes to such mind-boggling concepts. Case in point, there are different gradations of infinity, each level infinitely larger than the previous one. There are countable infinities, like the set of positive integers! And there are uncountable infinities, like the set of real numbers between any two points on the number line, no matter how small! Perhaps, most impressive of all is that there are an infinite number of levels of infinity!

Despite the general mathematical nature of infinity, Barrow shows how it finds its way into a multitude of human endeavors. How big is the universe? What does it mean to live forever, corporeally or spiritually? What would it take to time travel, and what might the consequences be given different structures of the universe and time (infinite, finite and boundless, or finite and bounded)? Are there other yous out there? What are the chances of finding intelligent life in the universe? And on and on. The infinite seems to be a surprisingly recurrent topic in human thought and for good reason.

There are times when the book requires a bit of concerted effort to understand, and on more than one occasion I found myself considering putting it down – not for lack of interest in the subject, but a distaste for the somewhat dense nature of some of the explanations. Points that I think should have been further explained, either through example or diagram, were not; others that I felt had been hashed out a hundred different ways found themselves once more under consideration. Barrow is clearly a scientist, and it seems odd that he would choose to skip over the more complicated details of things like topology and set theory, which are integral to making sense of the book’s main topic and its application to real-world interests.

Overall , though, I think it was well written and a definite read for anyone interested in the topic. If you’re afraid you won’t be able to understand the more intimate (mathematical) details of infinity – because you never took advanced math or you have, but never touched on set theory – you needn’t worry. Barrow covers the major details early on and with surprising clarity. There are a few topics (like the brief overview of general topology that prepares you for the chapter on spatial infinities) that even I found somewhat tough to follow; however, I don’t think it’s really necessary for the layman to know such things in order to appreciate the grander points being made. All in all, I think most people will benefit from reading The Infinite Book, and don’t feel bad if you find yourself asking what? after you’ve finished – it wouldn’t be worthwhile if it didn’t make you think.

[M.G. Mason · Rating 4 out of 5]

Infinity. How often do you think about it? I mean really think about the idea that something could go on forever? Have you thought about what the end of the universe might look like? Or whether there is a physical boundary to it? If there is a boundary, what is beyond it? More universes? Are they infinite?

What about the infinitely small? An atom’s radiation, for example, will never completely disperse, it will get smaller and smaller, halving each time while never reaching zero. This too is infinity and so too is a wheel that keeps spinning, unbroken by the things that would cause friction and slow it down. So many ideas behind infinity, it deals with an endless cycle, the infinitely large and the infinitely small and it is no wonder we take it for granted. Sometimes I wonder whether that is a good think; think about mathematical paradoxes a little too much, a little too often and it’s likely to make your head hurt.

That is why Barrow has written this fascinating book. It makes us really think about the concept of infinity and appreciate it’s place in the making of human civilisation – from mathematics and science to art and culture, the infinite has baffled us, well, um, infinitely. Since human civilisation first devised counting, we must have wondered whether their could be an upper limit. The answer is, of course, no but that hasn’t stopped people asking the question to begin with. All we need to do is add 1 to largest number we can think of and we have an even larger number. Infinity goes on forever.

This is the story of infinity, rather like an autobiography if a concept could have such a thing, from the height of the middle ages and the golden age of mathematics, this book is as practical as it is theoretical. It presents paradoxes to ponder and concepts to chew over. Sometimes, it gets quite heavy but the author tackles them in a way that doesn’t / shouldn’t put people off.

In many ways, it is not an easy read. You won’t need a background in physics but if you hated the subject or are one of those people who avoids popular science likes the plague, you may struggle through this. Try to stick with it though, because it is well written and engaging and you might just learn something.

See more book reviews at my blog

[B. Rule · Rating 4 out of 5]

This is a fun sampler of issues related to infinities. Barrow doesn't endeavor to give a systematic treatment of the subject, instead offering a discursive and entertaining tour of the history of the philosophical concept of infinity, quirks of the mathematical operations engendered by infinities (including a good, short Cantor explainer), cosmological speculations on the nature of the universe, its likely end, and the possibility of time travel, as well as a couple good knocks on the wisdom of seeking eternal life.

A lot of the material will be familiar to voracious readers of pop science and philosophy books, but it's assembled in a fresh way. Barrow doesn't stake out many firm positions of his own, but he gives fair overviews of lots of other thinkers. I'm always entertained by thought experiments on what it would mean for the universe to be infinite (or for the Many Worlds Hypothesis to be true), as the implication is that all possible existents will occur somewhere. Copies of us making every possible decision, and every possible decision tree flowing down from that, exist somewhere in infinity, if it exists. I guess I'm glad my consciousness resides in this local pocket of infinity where I could read this enjoyable book!

[Peter Grant · Rating 3 out of 5]

Given the subject matter, this book was always doomed to over promise and under deliver. I mean, infinity? How could that be dealt with in 300 odd pages. To my mind though, the under delivery was more than expected. Although there was some mathematical investigation and a look at the history of the concept, there was also a lot of dreary philosophical blather that just seemed like so much padding. I did enjoy some of the thought experiments, especially the one about a lamp being switched on an infinite number of times in a minute - and was it on or off after a minute - the sort of head scrambler I was looking for. One of the reviews on the cover said this was 'popular science at its best'; sadly, this was not true. In fact, the padding made it feel like this book was tending towards the infinite. Thankfully, this proved not to be the case.

[Sayantan · Rating 4 out of 5]

The first few chapters cover the philosophies of antiquity about infinity (Aristotlean, Christian etc.), so they are a bit boring and feels irrelevant. But their inclusion is justified by the fact that the author wants to include the development of ideas about infinity from the very beginning.

Then things start to pick up. The author covers a vast range of topics related to infinity: paradoxes, Cantor's set theory, and the (in)finitude of the universe.

But the best part of the book is some of the philosophical quandaries that the author introduces. The mind boggleth at the profoundness of some of the thoughts presented. Truly "Where science ends,philosophy begins."

Informative and thought provoking to say the least.

[Fortu · Rating 4 out of 5]

Relaxed and brief review of commonplace topics around the concept of inifinity, including references to the usual suspects in infinity-land: Cantor, Gödel, Turing, Einstein, and a bunch of greek philosophers.

Infinity is sometimes just an excuse to talk of other topics, mainly cosmology. A litle too much wandering around philosophical and religious issues for my taste, but nevertheless very interesting for the historical perspective. I´ve enjoyed the worthy notes and references.

Very advisable lecture if you have some background in calculus, physics and theory of computation, as you will most probably recognize the cases and backing concepts the author (too briefly) shows.

This is the firt J.D.Barrow´s book I read but certainly won´t be the last one.

[Andrew · Rating 4 out of 5]

The resourceful manager had begun by finding room for one extra guest in a full hotel, then a room for an infinite number of guests in a full hotel, but now he is being asked to find room for an infinite number of travel parties, each of which contains an infinite number of guests. What can he do? They will start arriving soon!

After a slightly meandering opening chapter or two this book starts getting going with "Welcome To The Hotel Infinity", an introduction to Cantor's fantastic diagonal proof and the infinite hierarchy of infinities. After which the narrative accelerates rapidly into realms of philosophy and cosmology, raising a huge range of questions that make you think long and hard. Recommended.

[Chelsea Lawson · Rating 4 out of 5]

I enjoyed this book a lot more than I thought I would given that it has no story or characters. It is, exactly as it says it is, an exploration of the concept of infinity as it has been explored in philosophy, mathematics, literature, religion etc over the years. It’s very well organized and I liked the pictures and thought experiments. Plus you get a bunch of mini introductions to famous minds that have worked on the puzzle of infinity. However, he also goes too far out sometimes and lost my attention like in the chapter about us being part of a simulated reality or when he gets into talking about immortality.

[Kevin · Rating 5 out of 5]

This was a really detailed and explaining book about infinity. It talks about infinity in multiple different ways, it talks about infinity paradoxes, infinity in math and number theory, the relative infinity. It even talks about hotel infinity, a word problem like hotel with infinite rooms. Personally, I found it interesting and fun to read. It was a bit confusing at times and was hard to keep up with everything the book was saying, however it was still good. I would recommend it to anyone who enjoys detailed interesting books and enjoy thinking while reading.

[Ayush Kumar · Rating 5 out of 5]

A fantastic book covering the endless scope of infinity. This is my first book of John D Barrow and I'm looking forward to reading his other books. He covers a diverse range of topics related to infinity and the arguments for and against it from both a mathematical sense as well as a physical sense.

A good book for amateur knowledge gatherers with references to thoughts and sayings by famous physicists, astronomers, theologists and the like. Would recommend for anyone looking to understand the basics of what infinity means or what it can mean.

[Marc94 · Rating 4 out of 5]

This book was pretty good, though a little repetitive at first. However, it made me realise how much more there is to infinities and it's really hard to truly grasp what infinity is. There are even different levels of infinities! The book later goes on to even examine whether or not we are in a computer simulation, topics on immortality, and finally time travel. I recommend this book to those that are curious about what could be out there.

[David Joseph · Rating 5 out of 5]

That this is the most easily accessible account of the "Universe of Discourse" can be easily argued and easily demonstrated and infinitely so.

It is elegant and artful.

You don't need to know any math at all to deeply appreciate the ideas that are explicated. A person just needs to have a working knowledge of plain English.

This is written at about, oh, Flesch–Kincaid Grade Level 8?

This is just a fine example of a little sumpin' for everybody.

Killer good!

[Attila · Rating 5 out of 5]

Most people think "infinite is just some really big amount". In reality, infinite is neither an amount, nor "really big". This is a great pop-sci book on infinites, presenting them in both mathematical and physical (and even in philosophical) sense. I recommend it to everyone who is interested in mathematics or science.

Those who have a good grasp of high school maths and physics may want to check only the last four chapters.

[AJ · Rating 4 out of 5]

A fun little exercise in the history and applications of infinity. Unfortunately, this book suffers from what I expect is the same in all layman guides to high-level mathematics, cosmology and astrophysics: any simplifications of these topics will leave more questions unless you take it all the way.

Regardless, it certainly was an enjoyable and accessible read.

[Mbuso Yende · Rating 5 out of 5]

Man has not seen God's eye-view on the concept of infinity, we can only approach it from one side, but here is a thought: if we have to traverse in opposite directions beginning at the same point, aren't we approaching infinity from both sides?...just a thought...the book has many thought-provoking ideas and concepts - a definite recommendation!

[AJ Ostrow · Rating 3 out of 5]

If you enjoy abstract theorizing about mathematical concepts and relating them to the human experience in analogies, or just enjoy mathematical theories and the history behind them, this book is for you. I liked it.

[Michael Soso · Rating 5 out of 5]

An excellent book covering all aspects of infinity: math, science, history, ethics, philosophy and theology. Too much ethics, philosophy and theology for my taste, but an excellent intro to the breadth of the topic. Barrows is an excellent writer.

[Natalia Nazeem Ahmed · Rating 5 out of 5]

Absolutely fascinating! The author provides beautiful descriptions of thoughts about the infinite - be it in science, mathematics, philosophy, or religion; and provides easy-to-understand descriptions of theories that surround the concept of Infinity. 10/10 would recommend.

[Iren · Rating 5 out of 5]

A comprehensive explanation of different paradoxes infinity brings us. It may be not a book for scientists, but it surely is for us amateurs of knowledge.

[Ilias · Rating 4 out of 5]

An interesting book that defines infinite and explains some mathematic paradoxes. Easy to understand for the most part.

[Jessada Karnjana · Rating 4 out of 5]

ประวัติศาสตร์ปัญหาค่าอนันต์ ค่าอนันต์คืออะไร มีจริงมั้ย เปรียบเทียบกันได้หรือเปล่า เรื่องเล่าทางคณิตศาสตร์ที่เขียนเน้นความสนุกสนานอ่านบันเทิง มีสมการพอหอมปากหอมคอ ไม่ทำให้ตาลาย

[Sarah Schmidt · Rating 4 out of 5]

Great read for people who love math theory. It took me a long time to get through the book because it's math heavy. It is a fun math read though.

[J.D. Steens · Rating 2 out of 5]

A few things caught my attention.

Barrow notes that Einstein was not comfortable with the implications of his theory that, in the extreme, gravitational centers are singularities. If spacetime is determined by the densities of matter within it, Barrow notes, then spacetime disappears when density is infinite and this is where the laws of nature break down.

Barrow states that in a black hole “density will be less than that of air.” P. 106. I didn’t understand that.

Barrow says there must be dark matter in a galaxy and it is calculated to be 10 x more than visible matter.* Here, gravity is seen as the cause of motion - in effect, it’s a reaching out, a grabbing, and a pulling of matter-energy. Aside from the fact that dark matter has not been found, Barrow does not clarify how Newton’s first law (inertia) is the inherent (self) movement of matter and energy and its possible implications for understanding galactic structure and movement. Namely, a gravitational center only receives matter and energy and it is inertial movement itself that supplies the movement that flows with space, per Einstein, toward the gravitational center. Seen this way, does dark matter need to be posited as an explanation for holding spiral arms in galaxies?

There’s a similar problem with Borrow’s positing of dark energy. After the big bang, he says that there’s deceleration as there’s only gravity “to slow it down” and that pulling effect lessens with distance so that, by 8 billion years, an anti-gravity effect takes over, resulting in the cosmos’ acceleration. But here, the anti-gravity effect is an X factor (non-discovered, illusive, “dark energy”) that pulls matter-energy outward in an ever-increasing manner. Characterized this way, he ignores the role of Newton’s first law of motion: Does the big bang create inertial motion of matter and energy that moves in an “all around” outward trajectory, and the inverse square law applies and accounts for the slowing down effect as it counters (the movement away from the cosmic gravitational center) the outward inertial movement? But at that 8 billion year point, or thereabouts, inertial motion, free of gravity’s effects, is free to continue its “journey” around cosmic curvature without the anchoring effect of a large gravitational center at the heart of the cosmos that holds it back.**

*Along with others, Barrow repeats dark matter’s “finding,” though there’s not been a finding as such, but, rather, some speculation based on some indirect evidence. The outer edges of galaxies rotate at about the same speed as the inner edges (Vera Rubin finding) whereas, with normal gravitational pull, the inverse square law says that the other edges must be slower than the rotating inner spirals. From this, he and others conclude, there must be a 10 x presence of extra matter in intergalactic space that pulls the outer edges and, thereby, keep them tucked into the galactic structure. Elsewhere he writes that, “Instead of being pulled by a force, objects follow the curves of spacetime.” This does not sync up with Barrow’s statement that dark matter pulls galaxies inward and keeps the arms from spiraling outward per Rubin.