The Unimaginable Mathematics Of Borges Library Of Babel Pdf

Open Preview

See a Problem?

We'd love your help. Let us know what's wrong with this preview of The Unimaginable Mathematics of Borges' Library of Babel by William Goldbloom Bloch.

Thanks for telling us about the problem.

Friend Reviews

To see what your friends thought of this book, please sign up.

Reader Q&A

Be the first to ask a question about The Unimaginable Mathematics of Borges' Library of Babel

Community Reviews

· 226 ratings · 35 reviews

Start your review of The Unimaginable Mathematics of Borges' Library of Babel

May 11, 2011 Paul Bryant marked it as probably-never

Book shelf enlargement is an issue that many men consider at some point during their lives. It is not uncommon for men to feel embarrassed or anxious about the size of their book shelves, from a young age all the way through life. The ladies do not like to see books stacked in corners of rooms, unsightly and hap-hazard. Fortunately, for the many men between the ages of 18-80 who are looking to add inches to their book shelves, there are a number of shelf enlargement products and treatments out Book shelf enlargement is an issue that many men consider at some point during their lives. It is not uncommon for men to feel embarrassed or anxious about the size of their book shelves, from a young age all the way through life. The ladies do not like to see books stacked in corners of rooms, unsightly and hap-hazard. Fortunately, for the many men between the ages of 18-80 who are looking to add inches to their book shelves, there are a number of shelf enlargement products and treatments out there. House furnishing research suggests that the average book shelf size is between 2 and 3 feet. But we here at Big Natural Shelves Inc believe that we are here to give nature a helping hand - the natural way. No drugs, and no pumps!

"Sturdy and ample"

However, book shelf enlargement products are not just for men who feel that their shelving is smaller than average. No matter what size your book shelf is, shelf enhancement products are designed to help you to be comfortable with your book shelf size and may help you to boost your reading performance and confidence at the same time. Length is important, true, but so is depth and stability for those hefty volumes - who wants his shelf to collapse suddenly in the middle of the night spilling pages and bending spines!

Big Natural Shelves Inc has been a leading provider of natural book shelf enlargement products for over 8 years. We make sure that all of the natural book shelf enhancement products that we stock have received positive approval from satisfied customers. Our natural book shelf enlargement supplements are designed with a specially formulated blend of natural ingredients which can help to increase wood flow to the book shelf, which can encourage expansion of the book shelf tissue. Our products also vastly improve reading stamina. We also supply products that can actually make you remember what you read for at least 24 hours! The girls will love you for it!
All our shelf extension products are delivered to you in plain brown wrapping. Paypal accepted.

Increase your shelf life today and bring a smile to that special lady.

...more

Aug 01, 2011 Kane Faucher rated it really liked it

The author does a very good job of explaining some of the mathematics that are implied from Borges' short story, and thus uses this as a generative point. The section on the manifold may be a bit confusing for many (although the author does give his frequent "advisories"). Perhaps a little too much time is spent in the beginning making qualifying comments / apologies when they may not be necessary. In my view, there were a few other avenues the author could have explored, but that is hardly cons The author does a very good job of explaining some of the mathematics that are implied from Borges' short story, and thus uses this as a generative point. The section on the manifold may be a bit confusing for many (although the author does give his frequent "advisories"). Perhaps a little too much time is spent in the beginning making qualifying comments / apologies when they may not be necessary. In my view, there were a few other avenues the author could have explored, but that is hardly considered a failing. ...more

"The librarian's life and the Library together embody a Turing machine, running an unimaginable program whose output can only be interpreted by a godlike external observer." "The librarian's life and the Library together embody a Turing machine, running an unimaginable program whose output can only be interpreted by a godlike external observer." ...more

Mar 12, 2011 Jonathan rated it it was amazing

This book is *awesome*! Why? The author takes a short story, "The Library of Babel," by Jorge Luis Borges and analyzes it along many different mathematical dimensions. The results are stimulating and accessible to non-mathematicians. The story is about a library, which is composed of:

An indefinite number of ... hexagonal galleries. In the center of each gallery is a ventilation shaft, bounded by a low railing. ... Twenty bookshelves ... line four of the hexagon's six sides... One of the hexagon'

An indefinite number of ... hexagonal galleries. In the center of each gallery is a ventilation shaft, bounded by a low railing. ... Twenty bookshelves ... line four of the hexagon's six sides... One of the hexagon's free sides opens onto a narrow sort of vestibule, which in turn opens to another gallery, identical to the first -- identical in fact to all.

What's the implication of this? The author, William Goldbloom Bloch, takes us through combinatorics, information theory, real analysis, topology and cosmology (a tough chapter), geometry and graph theory, and more combinatorics. He explains things in an easy to understand way, and then if you want more, has "Math Aftermath" sections that get more in depth.

In the end, he gives a long list of suggested readings. I have started a list here http://amzn.com/w/236UZ2PNNR3W2. What math books do you all suggest?

...more

Mar 25, 2017 Celebrilomiel rated it liked it

Recommended to Celebrilomiel by: Ellise

Fascinating, accessible, and thought-provoking.

In the first-person-singular sections that bookend the first-person-plural mathematical chapters, Bloch's prose had such a friendly and humorous tone that I liked him right away and went from merely intellectually open to fully invested and eager to see what he had to say on approaching Borges' short story through the lens of mathematics. He was like a best friend who delights you with his presence as well as his turn of phrase and makes you instan

Fascinating, accessible, and thought-provoking.

It seems that many people have a habit of skipping the front- and back-matter of a book, but I make a point of reading cover to cover, and this book proved why I do so: I enjoyed the acknowledgements more than any other I've ever read, and I'm glad I read the glossary, because he slipped in several sly quips. The nine central chapters on mathematics (and, later, literature analysis) did not carry the tongue-in-cheek style that the enclosing chapters did, since they were focused on the math and consequently were more straightforward, but his wit peeped through in a phrase here and a wry allusion there.

The chapters on mathematics were at times mind-boggling, as eponymously promised, but they were always understandable. Personally, I found the chapters on combinatorics, information theory, and graph theory the most interesting. The chapter on the topology of the library was intriguing, but the fourth dimension was a bit hard to wrap my mind around: it all made sense, the way he explained it, but trying to imagine it was… Well. You try to imagine the fourth dimension as physical space. The notion of the mirror-reversal in the 3–Klein bottle Library was fascinating, though — it made me want to write fiction with recursive multidimensional travel through mirrors.

Once I've studied higher mathematics and have an increased technical appreciation for the concepts propounded within this book, I think I shall come back to it and enjoy it all over again.

...more

Jan 05, 2011 Christopher rated it really liked it

Of all the short stories in Argentinian writer Jorge Luis Borges' masterpiece collection FICCIONES, "The Library of Babel" is one of the most peculiar. This weary narration by an aged caretaker of a library of seemingly infinite expanse involves several exotic mathematical principles, yet ones fairly easily graspable by the layman. The mathematician Bloch has written a fine book about all the thought-provoking concepts in Borges' story.

The complete text of "The Library of Babel" is included here

The complete text of "The Library of Babel" is included here, so if you like the intersection of maths and literature, you have all you need here to explore Borges' vision. Still, I'd recommend neophytes read this story first in FICCIONES, as there you'll also find some other enjoyable and influential short stories.

Each chapter discusses the relevant concepts in accessible prose, followed by a "Math Aftermath" for those who want to see rigorous figures and calculations. First we have combinatorics, namely how to calculate the number of possible books in the library. Bloch A remarkable conclusion is drawn, perhaps unrealized by Borges himself. If the library contained every possible book, even if only a single copy of each, then its contents would still be exponentially too large to fit in our universe. The second chapter concerns information theory, namely the (im)possibility of creating a catalogue for the Library.

In Chapter 3, Bloch discusses real analysis, with the springboard being Borges' footnote that instead of an infinite library, one could conceive of a single book of infinitely thin pages. A trip through non-standard analysis reveals a complication that Borges evidently didn't realize.

The fourth chapter discusses topology. The idea of the Library as a Pascal sphere is well-known to Borges fans, but Bloch also describes how a 4-dimensional sphere could meet Borges' description of an infinite but periodic universe. This is the most challenging of all the chapters, especially the Math Aftermath which talks about klein bottles and the like. You'll find this chapter much easier if you've read Edwin Abbott's FLATLAND.

Chapter 5, devoted to Geometry and Graph Theory, examines the honeycomb layout of the Library and possible paths through it, presenting multiple possible interpretations of Borges' text that have quite different ramifications for the inhabitants. The following chapter introduces more combinatorics to ponder how the disorder of the Library might be the Grand Order.

So as you can see, Borges' little story, that many people have no doubt read, thought "How cute", and moved on straightaway, touches on an immense amount of mathematical concepts. The final chapter is dedicated to informed speculation on just how much of the mathematical ramifications of the text Borges was conscious of.

My maths skills have seriously atrophied since I left school, but this was a friendly, approachable text, a catalyst for the all too rare utterance "Who knew maths could be fun!"

My only complaint is that Bloch occasionally goes off on flights of fancy that depart far from Borges' work, when a discussion rooted in the text is already more than enough to satisfy or overwhelm the layman. Also, there is a chapter dedicated to critics that he doesn't like, where he suggests that people stop looking at the text from certain literary criticism perspectives instead of venerating its mathematics.

...more

Feb 06, 2016 Brixton rated it liked it

*2.5/5

As a book of mathematics, this is an absolutely wonderful book! Very fun—very easy to follow for aspiring mathematicians of all calibers! Five out of five!

As a book on the literature of Borges, this is a terrible book. Incredibly reductive in its approach to the importance of mathematics in Borges' work. Very easily a one out of five.

This book was not so much an exploration of the intersection between mathematics and literature as it was a sort of fun excuse to explore some wonderfully co

*2.5/5

As a book of mathematics, this is an absolutely wonderful book! Very fun—very easy to follow for aspiring mathematicians of all calibers! Five out of five!

As a book on the literature of Borges, this is a terrible book. Incredibly reductive in its approach to the importance of mathematics in Borges' work. Very easily a one out of five.

This book was not so much an exploration of the intersection between mathematics and literature as it was a sort of fun excuse to explore some wonderfully complex mathematics in a digestible way. If you are solely interested in learning some basic number theory or think you'd like to explore higher dimensional topology and geometry, but are afraid because you might not have any math background, this is a book for you! Bloch does a wonderful job laying out complex ideas in a very approachable way. He rarely makes any assumptions at all about what his readers might know about math, and he moves from there. If you fall into this category, please by all means, pick up this book.

However, that being said, I'm not sure Borges himself would necessarily find this book entirely applicable to his Library of Babel. This book fails to explore the sheer mystery and mysticism of mathematics which Borges so clearly wished to bring to the forefront with his fiction. A sensitive approach to Borges' mathematical literature is one which explores our many interpretations of infinities, which investigates the arbitrariness of our often too unwavering mathematical axioms, our seemingly inbred fascination with the notion of number and the like. A sensitive approach to Borges' mathematical literature means asking what unimaginable mathematics means for our psychology and our humanity, like any other sort of literature. Borges' mathematics cannot and must not get bogged down with questions of the 3-torus and incomprehensibly large integers. As someone who enjoys math for math's sake, this was still a very pleasant read, but I felt as though I was betraying Borges' intentions as I read.

Read this book. I will recommend this book. This is what imaginative mathematics can and should look like, and this is by all means a great gateway into it. But please, if you pick up this book, read it with a grain of salt, and do not allow this to inform your understanding of Borges' infatuation with mathematics.

...more

A clear and straightforward explanation (for laypeople) of the complex and high-level math implicated in Borges' classic short story, "The Library of Babel." Though the story is just a few pages long--a fabulous translation, much better than the one I had previously read, is included in the beginning of this text--it raises questions from all different fields of mathematics, relating to the vastly huge number of books, the possible shape of the Library, and the textual combinations that might ap A clear and straightforward explanation (for laypeople) of the complex and high-level math implicated in Borges' classic short story, "The Library of Babel." Though the story is just a few pages long--a fabulous translation, much better than the one I had previously read, is included in the beginning of this text--it raises questions from all different fields of mathematics, relating to the vastly huge number of books, the possible shape of the Library, and the textual combinations that might appear therein. It's a nice and deep look into details that might be overlooked but deserve to be examined. In a later chapter, too, he provides some personal insights, which were really great: the comparison between Borges' librarians and the Turing machine is inspired and wholly correct, and I never would have thought of it.

In addition to lucidly treating concepts that might otherwise baffle, Bloch has clearly done a tremendous amount of research in preparation, and it shows. He addressing what seems to be the entirety of the criticism that's been written, and he writes of his experiences researching in Argentina. On top of it all, he provides an e-mail address at the end of the book, promising a more tailored reading list for those interested in the story!

"The Library of Babel" is really a beautiful work of fiction and a provocative thought experiment, and Bloch has given it here the treatment it merits.

...more

Jan 09, 2016 to'c rated it it was amazing

Recommends it for: Borges fans, math fans, and anybody else interested in expanding their mind.

One would have to write like Borges himself to praise this book adequately. I only grant five stars to books that expand my mind in some great and meaningful way and Mr. Bloch certainly succeeded in doing that. In many ways Borges' "Library of Babel" is one of his simplest and most accessible stories. The Universe as a gigantic library. Yet it is full of too much depth to be contained in that very library. Mr. Block now informs us that there is far more depth to be found than you may have imagin One would have to write like Borges himself to praise this book adequately. I only grant five stars to books that expand my mind in some great and meaningful way and Mr. Bloch certainly succeeded in doing that. In many ways Borges' "Library of Babel" is one of his simplest and most accessible stories. The Universe as a gigantic library. Yet it is full of too much depth to be contained in that very library. Mr. Block now informs us that there is far more depth to be found than you may have imagined. And he does so in a charming and very accessible manner. From simple combinatorics to Turing machines, each turn of each page yielded even more surprises. This is one of those books that causes me to dig deeper and follow some of the leads it contains. Even tho' I've finished reading the book it will be with me for a long, long time.

Interest in either Borges or math is not required.

...more

Feb 06, 2017 Craig rated it liked it

Quite accessible, but it jumps from concept to concept without really digging deep into anything.

Feb 17, 2013 Jafar rated it liked it

The Library of Babel is the best example of how Borges brilliantly weaved mathematical ideas into his fiction. This book explores some of the mathematical implications of this ingenious short story. Bloch has a great eye for spotting hidden idea in the story and then expanding upon them. The best was using the Library as a universal Turing machine.

Really quite good. Math for literature types, sort of. Explained to me, among other things, what a manifold is.

"The librarian's life and the Library together embody a Turing machine, running an unimaginable program whose output can only be interpreted by a godlike external observer. A user. A reader."

Really quite good. Math for literature types, sort of. Explained to me, among other things, what a manifold is.

"The librarian's life and the Library together embody a Turing machine, running an unimaginable program whose output can only be interpreted by a godlike external observer. A user. A reader."

...more

Sep 05, 2020 Nick Douglas rated it it was amazing

Answered several questions I had about the math implied by Borges's story, and introduced many other fun implications and counterfactuals. Almost entirely accessible without a post-high-school math background. And clever without getting too cute. Answered several questions I had about the math implied by Borges's story, and introduced many other fun implications and counterfactuals. Almost entirely accessible without a post-high-school math background. And clever without getting too cute. ...more

You will only enjoy this if you are a fan of both Borges and mathematics.

Sep 25, 2018 James rated it it was amazing

For those who want to dive deeper into the implications of Borges' famous library For those who want to dive deeper into the implications of Borges' famous library ...more

Can you believe i didnt pick this up on my own volition

Feb 07, 2021 Sevak rated it liked it

There are certainly interesting points in this book, but some parts can get really boring for people who know basic math.

May 21, 2021 Whittaker rated it it was amazing

The Unimaginable Mathematics of Borges' Library of Babel - Buy yourself a Ticket and the express-ride! The Unimaginable Mathematics of Borges' Library of Babel - Buy yourself a Ticket and the express-ride! ...more

Quick read. I really liked the gratifying story line.

Mar 11, 2017 William Schram rated it really liked it

This book applies ideas in pure mathematics to Jorge Luis Borges' short story, The Library of Babel. Given the description of the Library and the things mentioned in the story, we can come to a number of surprising conclusions about the Library itself. For one thing, it would not be possible to contain the Library in our Universe. The topology of the Library is also something of a sticking point for some since it is supposed to be infinite. Anyway, I thought this book was a charming introduction This book applies ideas in pure mathematics to Jorge Luis Borges' short story, The Library of Babel. Given the description of the Library and the things mentioned in the story, we can come to a number of surprising conclusions about the Library itself. For one thing, it would not be possible to contain the Library in our Universe. The topology of the Library is also something of a sticking point for some since it is supposed to be infinite. Anyway, I thought this book was a charming introduction to the mathematics involved and to the works of Jorge Luis Borges. ...more

Written by a talented creative writer, Borges fan, and mathematician--and any one of those on its own could be a full recommendation--this book delves into the mind-blowing implications of a short story that is already staggering in its implications of scale.
If you have the slightest interest in mathematics, Borges, or glimpsing infinity, I'd suggest you track this one down through a library system at once. I don't think there's another book like it in the world. It's such an unusual that I can Written by a talented creative writer, Borges fan, and mathematician--and any one of those on its own could be a full recommendation--this book delves into the mind-blowing implications of a short story that is already staggering in its implications of scale.
If you have the slightest interest in mathematics, Borges, or glimpsing infinity, I'd suggest you track this one down through a library system at once. I don't think there's another book like it in the world. It's such an unusual that I can't in good conscience run about accosting strangers and shouting "BUY IT!!", but it would look excellent on a shelf in your office, den, or waiting room.

Cross-posted from my longer review at Story Addict.

...more

Feb 01, 2015 Luke Duncan rated it really liked it

I picked up this book while working my way through Borges Labyrinths because 1) I've really been enjoying Borges and 2) this books was cited as being as compelling as GEB.

While it didn't quite live up to the GEB plug, it was pretty darn good. As someone with a kinda of mathy background in a technical field, I thought the first few chapters were a little weak but a nice warm up. I especially liked the chapter on Topology, which had the most in depth coverage.

I learned a few new things, got a goo

I picked up this book while working my way through Borges Labyrinths because 1) I've really been enjoying Borges and 2) this books was cited as being as compelling as GEB.

I learned a few new things, got a good book recommendation from the topology chapters references, and had fun with an easy read over a couple of days. I also found myself thinking "man I need to give this to a younger me! I'd totally have gone into math instead."

...more

Oct 06, 2011 Gill rated it really liked it

"Bloch is not only a mathematician, he's also a critic who has reviewed a lot of the literature on the Library of Babel and the life of Borges. So there is a lot in the book besides working out some of the mathematical implications of Borges' inspirations.

If you got as far as calculus in your math studies then you can probably follow most of the math without too much trouble. If you are a fan of Borges, there is a lot here about his math background and interests that you probably didn't know an

If you are neither, pass this by. Go read a lot of Borges and if you like him, then come back and read this.

...more

Oct 26, 2009 Joegjoeg rated it really liked it

Great book about the maths behind trying to make a library of every book that could ever be written. My favorite part of the book is in the preface when the authors asks "who is the intended audience for this work" and answers his question "Of the more than 6 billion people who are not Umberto Eco, I imagine that those who'd find this work appealing are..." Great book about the maths behind trying to make a library of every book that could ever be written. My favorite part of the book is in the preface when the authors asks "who is the intended audience for this work" and answers his question "Of the more than 6 billion people who are not Umberto Eco, I imagine that those who'd find this work appealing are..." ...more

Dec 31, 2010 Austin Savill rated it really liked it

This book is well written and shows many aspects of infinity as well as explaining much of what infinity means and how we can view or believe some things to be infinite. It explains the passage very well and analyzes many of the arguments of how Borgues conveys this library. I enjoyed it thoroughly but don't think many others would unless they enjoy math or explanations of philosophical concepts. This book is well written and shows many aspects of infinity as well as explaining much of what infinity means and how we can view or believe some things to be infinite. It explains the passage very well and analyzes many of the arguments of how Borgues conveys this library. I enjoyed it thoroughly but don't think many others would unless they enjoy math or explanations of philosophical concepts. ...more

Feb 27, 2015 Joseph rated it really liked it

Pretty neat little book. Uses Borges' Library of Babel as a springboard for introducing some interesting and relevant mathematical concepts in a more or less intuitive way. Though there's definitely some parts that require more concentration, this should be more or less accessible to anybody who's passed high school. Pretty neat little book. Uses Borges' Library of Babel as a springboard for introducing some interesting and relevant mathematical concepts in a more or less intuitive way. Though there's definitely some parts that require more concentration, this should be more or less accessible to anybody who's passed high school. ...more

Aug 31, 2008 Eoin rated it really liked it

Recommends it for: Borgesean Mathematicians

Ok, so I'm an easy mark for this book. I was concerned that this would be insufficiently mathy or literary or both, but it is a careful balance of readablity and high concept math. What the title promises, the book delivers. Ok, so I'm an easy mark for this book. I was concerned that this would be insufficiently mathy or literary or both, but it is a careful balance of readablity and high concept math. What the title promises, the book delivers. ...more

Jan 07, 2011 Thomas Fackler rated it really liked it

A concise exposition of the mathematics we can employ to orient ourselves in The Library.

May 11, 2012 Stephen rated it it was amazing

Fantastic, non-trivial analysis of Borges' story, comes complete with topology, combinatorics out the wazoo, with just a hint of non-linear dynamics. Fantastic, non-trivial analysis of Borges' story, comes complete with topology, combinatorics out the wazoo, with just a hint of non-linear dynamics. ...more