The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

by Paul J. Nahin

How two pioneers of math and technology ushered in the computer revolution

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use―from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer , Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras―mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon―advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

Genres: Science, Mathematics, History, Nonfiction, Computer Science, Biography, Computers

248 pages, Hardcover

First published January 1, 2012

About the author

Paul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire and the author of many best-selling popular math books, including The Logician and the Engineer and Will You Be Alive 10 Years from Now? (both Princeton).

Reviews

[Paul · Rating 2 out of 5]

The biggest problem with this book in general is that I'm not at all sure what the audience for it is. I was expecting something of a dual biography with some information about information theory. In fact, there's a brief chapter at the beginning that's a bio, but then it's about 8 chapters which are basically just a light textbook on electronics and information theory - kinda like a series of lecture notes for a 1 or 2 week introductory summer school course. The book ends with a terrible introduction to quantum computing (the author drags up old tropes about "spooky action at a distance" - which are half a century old and almost certainly designed to make you try to not understand what's going on), followed by some kind of weird, not very good short story about a "language de-clarifier" that I think the author himself wrote. The short story actually gets a lot of the underlying science wrong as far as I can tell, despite apparently being authored by someone writing basically a textbook on the subject.

I think that people with a casual interest in the subject will quickly get lost in the proofs and diagrams and whatnot, and people with a more sustained interest should probably read a better textbook. I think all the same information and more is contained in the eminently readable Quantum Computation and Quantum Information by Isaac Chuang and Michael Nielsen - one of the only textbooks in my years of education that I actually sat down and read cover to cover. Admittedly that book has more of a quantum information skew, but that just emphasizes how light on details this book actually is.

As for the audiobook specifically, it is a complete mess. DO NOT USE THE AUDIOBOOK VERSION OF THIS BOOK. The book is like 30% mathematical equations, and the person reading it doesn't even know how to pronounce a mathematical equation - for example P(A) is pronounced "P parenthesis A" rather than "P of A", lim(k->Inf) is pronounced "limit k right arrow infinity", it's very, very distracting. He mindlessly reads out 8x8 matricies as if we were rain man, able to mentally fill in a 64-position chart in our heads. I was able to follow what was going on only because I've taken classes in this subject and was familiar with the proofs. There is a reference guide accompanying the book which might help (though in that case you're basically going to have to ignore the guy speaking as he reads out all the values on a table or whatever), but if you're going to be sitting there looking at figures (the book relies HEAVILY on figures) the whole time, you might as well not listen to the audiobook at all and just get it on Kindle or something.

The only good thing about it is that except for the last two chapters, he's not really wrong about anything, he just goes into too much detail. At first I thought I was going to like this book, since usually these types of books have the opposite problem. That said, I don't recommend this book because as I said before, I can't imagine who would want to read it.

[Jim Razinha · Rating 2 out of 5]

Deceptive title..I should have read the reviews...thought I was getting a semi-biographical piece. If I wanted a book on logic, I would have picked a book on logic. One chapter on the two and very loose references to them during the remainder electronic/logic discussions. Look elsewhere if you actually want to read about those two fascinating men.

[Lucille Nguyen · Rating 2 out of 5]

Disappointing. Too technical to be readable, and the technical parts were rather poorly written for any sense of comprehension. Some fun introductory logic problems with some... choice comments about mathematicians and philosophers. Ultimately rather fails to live up to its aims, recommend reading a book about Shannon or Boole instead, and additional topics on information theory, mathematics, and logic.

[Josh Friedlander · Rating 4 out of 5]

A brief biographical survey of the two title characters (George Boole and Claude Shannon) is followed by a dive into how they created modern computing (Boole's algebra of binary variables - which originally goes back to Leibniz, like most things - and Shannon's idea of encoding them into electric relays which could thus represent arbitrary calculations). The book is theoretical (opting to always use relays - a switch whose state is determined by whether current is passing through it or not - as Shannon did, not the solid-state semiconductors in integrated circuits used in most electronic applications today), but as befits an Electrical Engineering professor, it is full of technical terms of art (p-n junction, bi-stable latch, clocked RS flip-flop...)

Given a small "vocabulary" of logic gates (NOT, AND, OR, XOR, NAND, NOR, XOR, XNOR), Nahin demonstrates how to carry out all integer arithmetic, and how to create persistent storage (finite-state machines) in electronic circuits. Chapter Six explains how Shannon used Bayesian conditional probability to reliably compensate for degradation of electronic components ("crummy relays") through redundancy, as well as the more general information theory behind reliable communication through noisy channels. (Fascinatingly, Shannon's work was explicitly influenced by a paper by von Neumann in which he speculated that machines could make decisions in situations of uncertainty modeled on the neurons in the brain, taking a majority vote of its inputs - a direct ancestor of today's neural networks.) Shannon's Bell Labs colleague Hamming realised that this problem is directly related to geometric question of sphere-packing: how many spheres in n dimensions can be packed together so that they are touching? It turns out that the number is pleasingly high in dimensions four and twenty-four, though no-one knows why. The last technical section is about the oscillating clock signal which keeps time for a processor's operations. (This is why CPUs are measured in frequency, or Hertz.) Although it is possible to let instructions propagate through the circuit as soon as they happen (asynchronously), this can lead to unexpected behaviour. (It is also possible to "overclock" a CPU: gamers do this, but it can lead to memory issues and hardware damage.)

Nahin promises that the book is accessible to a "technically-minded high-school junior" (but, he adds, not to "high school dropouts"). I found the maths mostly okay but the electrical circuits more challenging, frequently needing to double-check the function of diodes, capacitors or pull-down resistors. The audiobook format isn't ideal for this. The circuit diagrams are included in a PDF, but the narrator reads out reams of equations (and even, bizarrely, eight-by-eight matrices row by row) which are much easier to grasp when seen. I would question how many high schools teach, say, the Hermitian adjoint of matrices - not mine at any rate.

The last two chapters are more philosophical, discussing the limits of computation. Firstly, a "Turing machine" can only compute countably infinite sets of numbers, excluding for example the set of the real numbers. Secondly there are physical limits: the speed of light, and the fact that information is actually destroyed by a calculation (since the inputs are lost, except in the case of an output with only one possible set of inputs). Nahin discusses reversible logic gates, and the possibility of fully reversible computing using only these. This is noteworthy in light of an intriguing comment by von Neumann that the minimum energy required to manipulate a bit of information is exactly defined in terms of temperature and Boltzmann's constant (connecting entropy in its information sense to its thermodynamic sense). This may imply that fully reversible computation would produce less heat than this, with potential implications for chip performance. The last sections of the book cover the spectre of quantum computing. After explaining the theory and the implications of being able to find prime factors in polynomial time*, Nahin tackles the reality behind the hype. Like fusion power, practical quantum computing seems forever in the future. But seeing how quickly classical computing went from NAND to Tetris (or Shannon to iPhone) ought to force us to keep an open mind. Still, it is hard not to raise an eyebrow at the time traveling Bilking paradox...

* Summarised in this whimsical limerick by mathematician Peter Shor:

If computers that you build are quantum
Then spies everywhere will all want ’em
Our codes will all fail
And they’ll read our email
Till we get crypto that’s quantum and daunt ’em.

[Jigar Brahmbhatt · Rating 3 out of 5]

While replete with challenging mathematics, what the writer attempts here is to place George Boole and Claude Shannon at the forefront of the information age.

Boole famously invented the Boolean algebra in early 1800s, supplying mathematical symbolism to logical arguments so that the limitations of classical Aristotelian logic (all men are mortal, Socrates is a man, so Socrates is mortal) could be turned into a formal useful system.

Boolean algebra had to wait for hundred odd years until a young American electrical engineer could find an application of it in electrical circuits. Claude Shannon envisioned that electrical circuits could be made to perform logical operations. The book delves into the technical aspects of how that happens, because to appreciate the beauty of what Shannon achieved one has to be aware of some technicalities. That seems to be the off-putting aspect of this book for a lot of readers. Because the mathematics and electrical notations used can be heavy for non-technical readers, and they can miss out on learning about a very interesting man. I was wondering whether all of it could be reduced into an easily understandable language sans the mathematics, but that seems impossible too. No matter how obvious Shannon's invention sounds today it was a feat of imagination. The logical gates that form the core of computers were very much the brainchild of this curious man, who spent his free time inventing useless gadgets (search for Ultimate Machine by Claude Shannon on youtube if you can. It is a machine whose only purpose is to switch itself off, and if you spend more time with it you will start thinking that there is a dark, mysterious force residing inside it.)

The book is a bit odd though. People who are technically inclined have already learned most of it in colleges or through proper course books, while the curious layperson has to struggle to penetrate it. My take is that it made me saw something that I had missed for so long: that combining electrical circuits with something as far fetched as Boolean algebra was no minor feat. Shannon's 1948 paper "A Mathematical Theory of Communication" is called the Manga Carta of the information age, but when asked in an interview about his achievements he modestly said that not many people were aware of both these fields at the same time then. Well, how simple he made it sound!

[Brian Clegg · Rating 3 out of 5]

For its target readership this is an excellent book – and I have to say as someone outside that market I really enjoyed some parts – but the fact remains it is aimed at a pretty narrow segment. There’s even a little section at the front of the book that effectively says ‘read this to see if you can cope with the rest.’

The bits I found particularly appealing were a few introductory logic problems (though I’m not sure I agreed with all the conclusions) and the pocket biographies of mathematician George Boole and information engineer Claude Shannon. However, while technically qualified to deal with the other parts of the book, in truth I couldn’t be bothered – it was too much like hard work.

For bits of it I would have to wade through far too much grunt maths, and for other bits would have had to think far too hard about electronic circuits and the logic circuits beloved of basement dwellers on computer science courses. (Or was it just my university that confined the computer scientists to the basement?)

I think the author makes the mistake that many academics make when trying to write for a broader audience: they carry through too much of the textbook, and find that the aspects that often encourage people to remember things in that context (often because they involve repetitious grunt work) actually prevent popular science readers from getting the message. It’s a shame, because the subjects are interesting, but unless you are the kind of person who designs logic circuits for fun, this is probably not the book you’d want to see.

Review first published on www.popularscience.co.uk and reproduced with permission

[Behrooz Parhami · Rating 5 out of 5]

[I wrote this review on June 25, 2013, and posted it to GoodReads on June 25, 2022.]

Despite what one might think from its title, and classification by our campus’ library at UCSB as “biography,” this book isn’t a double-biography of two computing pioneers. Rather, it is a technical book that puts the contributions of mathematician George Boole (to Boolean logic) and electrical engineer Claude Shannon (to switching circuits and information theory) in perspective, connecting them to each other and to modern topics such as thermodynamics of computing and quantum information processing.

The author tries to explain some concepts in gentle, nontechnical terms, but it is fair to say that readers not already familiar with Boolean algebra, switching circuits, and information theory will find it difficult to follow all the details. For computer science/engineering students and professionals, however, the book is quite useful as background reading and for grasping the importance of the collaborative nature of the work by Boole and Shannon, even though they lived a century apart. Shannon, who idolized Boole, effectively put Boole’s ideas into circuits, creating the fields of switching circuits and information theory.

Early in the book, the reader is exposed to the use of Boole’s formalism for solving logical reasoning problems, with the appropriate cautionary note that logical reasoning isn’t a cure-all. A number of examples are given where using Boole’s notational convention helps make what seems like a complex problem easily tractable. Then, the following interesting example of a paradox/puzzle is provided on pp. 8-9.

An experienced lawyer agrees to teach law to a young man, who signs a contract to pay $1000 up front and another $1000 when he wins his first court case. Several months pass after the training is over and the young lawyer doesn’t begin his career. The teacher becomes impatient and sues his former student for the $1000 owed. He tells the young man, who has decided to argue his own case, that he might as well pay up before the trial, because if he loses the lawsuit, he will have to pay by court order, and if he wins, he will have to pay according to the terms of the contract he signed. The trainee counters that he does not have to pay at all, because if he prevails in court, he owes nothing per court’s decision, and if he loses the case, he still owns nothing according to their contract. Who is right?

Try to solve the paradox/puzzle above before reading the explanation that follows. The outcome of the challenge depends on whether the contract or the court decision is supreme. With the contract being supreme, the teacher loses his money if he wins the court case and gets the money if he loses. With the court decision being supreme, however, the teacher gets his money if he wins the lawsuit and forfeits the money if he loses the case. In the arguments above, each side mixed the two interpretations to suit his purposes. Absurdities such as this one arise in a number of situations when a concept or statement is applied to itself, the simplest example being the truth or falsehood of the statement, “This statement is false.”

One of the interesting side notes in the book (p. 132) pertains to Hamming’s single-error-correcting-code, which is well-known and rightly attributed to him. However, while Hamming’s publication of his idea was delayed by Bell Lab’s legal department as part of their patenting strategy, Shannon independently discovered and published the code in The Mathematical Theory of Communication (1949).

The author also reviews some ideas pertaining to Turing machines and the role they have played in the study of computation, although, appropriately for his style and target audience, he does not provide much detail. Examples include the fact that any computable function can be computed by a 2-state or 2-symbol Turing machine (p. 167) and the equally surprising fact that there exists a universal Turing machine with 6 symbols {0, 1, A, B, X, Y} and 21 states, not counting the halting state (p. 168), that can emulate any other Turing machine using a stored description of the latter (a program).

An example of recreational math problem with significant theoretical and practical consequences is the Busy Beaver problem, so named by mathematician Tibor Rado (p. 167). Consider a Turing machine with the 2-symbol alphabet {0, 1} and n states, plus a halting state, starting with a “blank” tape containing all 0s. What is the maximum number of 1s that the Turing machine can print on the tape before halting? We can denote the number using the function BB(n). We know that BB(3) = 6 and BB(4) = 23. However, beginning with n = 5, the value of this function is unknown. We know lower bounds, such as BB(5) >= 47,176,870 and BB(6) >= 10^(10,566). The value of BB(10) is such a huge number that we can’t even write down a lower bound for it without inventing a special mathematical notation. The function BB is noncomputable.

Quantum information and quantum computing are discussed briefly as tools for overcoming certain inherent limitations of conventional computing devices. An interesting poem by one of the pioneers of quantum algorithms is used to lighten up the discussion of quantum computers. Shor’s poem is: If computers that you build are quantum, / Then spies everywhere will all want ’em. / Our codes will all fail, / And they’ll read our e-mail, / Till we get crypto that’s quantum and daunt ’em (p. 190).

The book ends with an epilogue (pp. 210-218) which contains a wonderfully funny description of a useful gadget for the information age: the anti-amphibological machine (or in plain English, the language clarifier). Upon receiving a batch of divorce papers which he can’t understand, an inventive man teams up with his former professor to design a machine that receives incomprehensible, convoluted text as input and produces a straightforward and clear translation as output. The inventing team puts a prototype of its machine to the test by feeding it with the following speech of an academic dean:

“Even in institutions like our college, which may be expected to have rather homogeneous populations, one encounters a tremendous diversity in the family subcultures that students come from, in addition to the idiosyncratic mix of assets and liabilities that characterize them. … We thus encounter students whose educational aims are crystal clear, as well as others whose purposes have all the clarity of an amorphous mist emanating from a thick cloud of existential miasma.”

To their delight, the machine spits out the following clarified translation:
“No two students are alike … Some students know what they want, and others don’t.”

Over time, lawyers become enthusiastic users of the machine, after it is tweaked to work forward as well as backwards, thus allowing simple texts to be converted to legal documents. Then, the US Department of Defense shows interest in the machine and offers its inventors $1M per year to transfer the technology to them and forget that the machine ever existed. The inventors put the Pentagon proposal and suggested contract through the machine; hundreds of pages of terms and conditions, and pertinent articles of law, are translated to:

“Sign the agreement, forget you ever heard of the Language Clarifier, and you get a megabuck a year for life. Don’t sign the agreement, and they toss you in the slammer (with one 60-second cold-water, low-pressure shower every 10 days) and throw away the key.”

I found only one serious error in the book. After describing a 10-state solution to the puzzle of two adults and two children wanting to cross a river in a boat that can hold only one adult or two children (p. 141), the author notes that if the children and the boat were to remain on the same side of the river where they started, while the adults end up on the opposite side, an eleventh state or step would be needed (the children going back in one crossing). However, the 10-state solution already contains the desired state right before the final state; thus, only 9 states would be needed for the modified puzzle.

I enjoyed reading this book and learned a great deal from it. The book has my highest recommendation for those who study about or work with computers and information technology.

[Maurizio Codogno · Rating 3 out of 5]

Il titolo del libro sembrava promettente, anche se non riuscivo esattamente a capire cosa avessero in comune George Boole e Claude Shannon oltre che essere stati scienziati. All'atto pratico, però, la parte più strettamente biografica è davvero ridotta, e Nahin si mette a scrivere di elettronica di base, da ingegnere qual è, non perdendo occasione di ricordare che la matematica è una scienza arida... citando James Gleick (L'informazione) che è sì un giornalista ma scientifico, e quindi direi non certo prevenuto. A un certo punto mi è sembrato di leggere un libro di testo, anche per le note del traduttore Ciro Castiello che ha spesso aggiunto i passaggi logici che venivano dati per scontati. Devo però riconoscere che nella parte finale del testo la spiegazione dell'entanglement quantistico è la più chiara che abbia mai visto: ma che ci azzecca con i due (almeno in teoria...) protagonisti? In definitiva, un libro per ingegneri ;)

[Chris Esposo · Rating 4 out of 5]

This is a very good book with one caveat: it's really not best consumed in audio format. Although one may try, and it would be a good practice in listening-comprehension skills, to really grasp the book, you need the diagrams and printed formulae, which are provided in a 170-page pdf attachment (not all full pages).

That being said, "The Logician and the Engineer" is a well-written tour of elementary Boolean Algebra and Shannon Information, and how the two of those subjects inform the building of the Turing machine and the digital computer, with all predicative material required, built or explained included with either a formal proof (more or less always in specific small tuple/small index cases), or an illustrative example. The book does go into some decent detail into what it means for there to be infinite numbers in a computer system, what it means for numbers to be dense, to be computable, and even goes through the Cantor diagonalization argument to show different number system cardinalities, which usually stumps the math student taking intro to analysis for a little while, so it's not the easiest material.

Most of the basics of Boolean algebra, however, can be proven by constructing a truth table, and the only topic really covered with respect to the Shannon Information is Shannon entropy. So its a good intro to that material, but not a thorough one. That being said, the material is only watered down, when it's practical to do so. Thus for someone that is totally new to this subject reading this text, if they get it all, they will come away with a workable knowledge of the subject.

I can't say I got everything the first time I listened to it, as the reader does a literal read of the material which becomes very challenging when the author goes through say an equational proof and the reader reads out each component of the equation, parenthesis, ellipsis, and all, at each step. With all the symbol accounting, including a reduction to terms, and whatever algebraic sleight of hand that may pop up, you'll have to keep a lot of terms in your head while listening. Things get hairier when a graph or circuit diagram is explained.

The sections on error detection and how sequential state machines work were especially interesting to me, with the latter being useful as a basic backgrounder for computer system builders and hobbyist who like to overclock their machines, and how that works in computers.

A brief foray is made at the end on information destruction (basically surjective mappings of data) and how that bridges Shannon entropy with thermodynamic entropy - what is meant physically for information to be destroyed. That was interesting. And the other final topic is quantum information, which I'm not sure anyone who hasn't seen that material would get easier, especially since the author throws in terms like self-adjoint and uses the bra-ket notation, with the only explanation being "I presume all high schools now cover matrices, and therefore will proceed in that manner". Lazy assumption to make, given the unfortunate decline of secondary school education over the past 10 - 15 years. Nonetheless, the material was interesting.

I still recommend this book, it's about 1/3 history 2/3 mechanics, written to be as accessible as something like this could be, and could also be useful to people working with the material professionally for reinforcing comprehension.

[Parthipan Jayaram · Rating 3 out of 5]

Boole notably developed Boolean algebra in the early 1800s, providing mathematical symbols to logical reasoning, overcoming the limits of traditional Aristotelian logic.

Boolean algebra had to wait almost a century before a young American electrical engineer discovered its use in circuits. Claude Shannon proposed making electrical circuits perform logical processes. A technical understanding of how that occurs is required to appreciate Shannon's achievement. That appears to be the stumbling block for many readers. Non-technical readers may lose out on learning about a fascinating guy due to the mathematics and electrical notations utilized. I wondered whether it might be reduced to a simple language without the mathematics, but that seems impossible. While Shannon's innovation may seem apparent now, it was a creative leap. This inquisitive guy who spent his spare time creating worthless devices created the logical gates that make up the core of computers.



But the book is strange. For the inquisitive layman, it is difficult to understand since it is not taught in colleges or textbooks. It made me realize that integrating electrical circuits with something as far-fetched as Boolean algebra was no small accomplishment. However, when questioned about his accomplishments, Shannon humbly said that not many people were aware of both areas at the same time. How easy he made it seem!

[William Schram · Rating 3 out of 5]

The Logician and The Engineer is a book by Paul J. Nahin. It covers the engineering aspect of logic gates and applications of information theory.

Here I am, typing this review on a laptop. Later I might update it on my phone, but the shared structure of logic gates and electronics underlies both devices. The theory of logic is ancient, but applying the power of mathematics to it is somewhat recent. George Boole wrote his masterpiece on mathematical logic back in 1854. The book failed to find an audience at the time. On the other hand, we have Claude Elwood Shannon, a man appreciated in his time.

I skimmed parts with Truth Tables, but I enjoyed the biographies. In the epilogue, Nahin discusses a story about a machine that clarifies text. It finds the fundamental meaning of an abstruse passage and presents it in clear English.

I enjoyed the book, but it wasn't my favorite Nahin work. Thanks for reading my review, and see you next time.

[Cassie Thompson · Rating 2 out of 5]

Even without a technical background, I found this book enjoyable. I especially liked chapters 1,2, and 10 which were the most accessible to me. The puzzles/thought experiments were fun.

HOWEVER...
I was going to give this book 4/5 stars, but that godawful, sexist story in the epilogue really left a nasty final impression. Does not reflect well on the author. ("As the pretty young lady left, Willard found himself admiring her slender ankles, the motion of her firm thighs under a snug dress, her really spectacular bottom." Seriously, dude?)
You may have been born in a different time, Mr. Nahin, but that sort of humor has long since been found distasteful. And even if you and your friends don't find your chauvinism embarrassing, remember that women read your books.

[Roberto Rigolin F Lopes · Rating 5 out of 5]

This is an unusual book. About two unusual thinkers, Boole (1815-1864) and Shannon (1949-2001). Boole established logic as a branch of mathematics. Shannon used Boolean logic to design electronic circuits and ignited Information Theory. We are in 2012, Nahin is connecting together the achievements of both thinkers to our information age. To do so he describes with some depth a wide range of topics starting with Boolean logic and digital circuits. Passing through probability theory, information theory and Turing machines. To end up with thermodynamics of information and quantum computing. Out of my comfort zone therefore unusually fun. Thus demanding an unusual curious reader. Is that you?

[Duhart Vader · Rating 4 out of 5]

This a very good book to know about Boole and Shannon but, as all technical audiobooks, it is quite hard to follow the technical bits and even harder to imagine the Karnaugh maps to which he refers... so I recommend the printed version better.

A small rant: he says that the "engineer's proof" of Boole's inequality is easier than the induction one. This may be true but he's assuming he can count the elements that form the events while Boole's inequality is true even if the sample space is uncountably infinite.

Finally, I do use ChatGPT as a language simplifier... it's funny to listen that just 10 years ago that was sci-fi stuff.

[Robert Mason · Rating 3 out of 5]

I would rate this higher if it fixed it's focus. Throughout it wants to be a scientific biography of the work that connects Shannon and Boole - and at times the connection is really shoe horned in despite a tenuous connection - but it is not really a scientific biography. If you read it as a book building up basic ideas for computers from the abstract logical Boolean algebra as applied to circuitry by Shannon then it is a really enjoyable book, with small biographies of the two mathematicians mentioned. It is a story of the ideas not the men who had them.

[John Price · Rating 3 out of 5]

There's some interesting stuff in here, and I enjoyed revisiting the logic bits from my second year hardware course. I appreciate the author's aim of writing for an educated audience, but I found most of the math liberally sprinkled throughout more distracting than anything. Yeah, it's technically "only" highschool or first year algebra, but that was 20+ years ago. I wouldn't call it especially interesting math; it's just kind of there.

Or maybe its just that sigma notation triggers my Calculus 2 PTSD.

[Ross Nelson · Rating 3 out of 5]

Like others, I found the title deceptive. The book is more about electronics than the rise of the information age, and there's only a few chapters devoted to the men named in the title. Disappointed.

[Miguel Panão · Rating 3 out of 5]

The first chapters are great, but after chapter 7, the author begins to deviate a lot from the initial idea of the relation between Boole and Shannon, and we would win a lot if he had used the Language Clarifier of the end story.

[Robert Koslowsky · Rating 4 out of 5]

In October 2009, Claude Shannon was a featured Innovator of the Month in "A World Perspective" newsletter. He is considered to be the father of information theory. Through his work, Shannon informed engineers that when a message is properly encoded, it could be transmitted across a noisy channel with an error rate below any predefined level. Common examples of noisy channels to be overcome include static on a telephone line and cosmic rays inducing a mutation in a strand of DNA.

I followed this feature a year later with an October 2010 article on George Boole as the Innovator of the Month. His groundbreaking work on logic led him to develop a different algebra: one where algebraic operations were performed on symbols representing entities or classes. Boole possessed an uncanny knack for perceiving that the symbols of operation could be separated from those of quantity and then treated as distinct objects of calculation.

Claude Shannon studied this Boolean algebra almost a century after it appeared and developed the idea of encoding logical relationships (such as OR and AND relations) in an electric circuit. He recognized that Boole's work could form the basis of mechanisms and processes in the real world of communications. In 1937, Shannon wrote his master's thesis at MIT, showing how Boolean algebra could optimize the design of electromechanical relay systems, then used in telephone switches to direct phone calls. Shannon also demonstrated that circuits with relays could solve Boolean algebra problems. By using the properties of electrical switches to process logic, where ON = 1 or TRUE and OFF = 0 or FALSE, the basic concept underlying all modern electronic digital computers was developed. Hence Boolean algebra became the foundation of practical digital circuit design. It could be said that George Boole, via Claude Shannon and his successors laid the theoretical basis for the Digital Age.

Paul Nahin’s 2013 book, The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age, was an intense read, but follows the same line of thinking as above. He links the displaced-in-time contributions of George Boole and Claude Shannon who, together, set the wheels in motion for the ongoing digital information revolution. Nahin writes, “Modern engineers view Shannon’s ‘Mathematical Theory’ as his Principia, an achievement even greater than his switching theory use of Boolean algebra . . .” The transmission of digital data, which is common today with the ever-increasing use of the Internet, for example, is at the heart of Shannon’s work. In “Mathematical Theory,” he lays out for engineers, as Nahin describes, “the theoretical limits on the transmission of information from point A (the source) to point B (the receiver) through an intervening medium (the channel) . . . In a perfect world the digital stream would arrive at the receiver exactly as it was sent, but in the real world the channel is noisy and so, occasionally, a bit will arrive in error. That is, now and then a transmitted 0 will arrive as a 1, and vice versa.”

But that, as it turns out, is not a major difficulty. “There exists,” as Nahin writes about Shannon’s findings, “at least one source encoding procedure such that, no matter what the channel noise may be, the error rate at the receiver can be made arbitrarily small. But even with an arbitrarily small error rate, it isn’t zero, and thus there will be errors. So, at the very least, the receiver would find it useful to be alerted when an error does occur . . . That can be done quite easily with what is called parity.”

We won’t get into the details of how “parity” is implemented and used in digital design, suffice to say that parity violations produce and alert that something is wrong with the signal. That is good, but as Nahin writes, “wouldn’t it be even better if our digital logic could fix errors? Of course it would! . . . In fact, however, error correction is possible and, indeed, it’s not even particularly hard to achieve.”

Shannon’s work didn’t include developing source encoding-decoding schemes with associated error correction schemes, but many others followed in his footsteps. In the almost 70 years since the publication of Shannon’s “Mathematical Theory,” a number of coding schemes – Reed-Solomon codes, Hamming codes, BCH codes – have achieved error rates very close to Shannon’s defined theoretical performance limits.

Brush up a bit on your high-school algebra, early college statistics, and refresh yourself on basic electric circuitry and you’ll appreciate the work Nahin has done in presenting the synthesis of Boole and Shannon he brings forth.

Those involved in the field of computing and engineering leveraged this knowledge during the middle of the 20th century, and today, society benefits from the ubiquity of digital appliances that pervade our lives. As Nahin writes, “What Boole and Shannon created, together, even though separated by nearly a century was without exaggeration nothing less than the fundamental foundation for our modern world of computers and information technology.”

It's a Good Read!

[Karthik Shashidhar · Rating 3 out of 5]

Started off promisingly with biographies and puzzles, but then ended up being virtually a textbook of electrical engineering!

[Nate Freiman · Rating 5 out of 5]

Challenging, loved it. Amazing to read the short story at the end, written in 1979, satirizing the problem of “the language clarifier” anticipating LLMs..

[Mark · Rating 4 out of 5]

I picked this up on a whim with no research. Shannon is trendy in these days of "Big Data" for his theory of information, and skimming the book it looked like a general history with maybe a bit more technical details than normal. This is more about Shannon as an engineer, though, and Boole of boolean algebra fame as a theoretician.

The early bit is biographical, but it's really just the first bit. Writing is good and full of nice tidbits about two geniuses. Favorite story: Boole got a bad cold that he got after getting soaked in the cold rain then teaching a class in his soaking clothes. His wife was into homeopathy so she figure the best cure was to treat it with more cold and wet, wrapping him in wet blankets. He didn't recover.

After the biography there as a bait and switch. There's are wiring diagrams and a nice chunk of math, and even if the math is sub-calculus I had to pull out a pencil and paper many times before I "believed" an interesting passage. You can get through it with just motivation and high school math, but I feel like a lot of the material was written as if it was intended for a freshman engineering student.

Or perhaps for a 40-something occasional programmer who never really worked through the circuit design of a memory bit, which is coincidentally exactly what I am. And I'm kind of happy that I now could work out how to design digital memory circuits if I ever were sent back in time. (There's actually a very short windows where this would be useful, maybe a few years on either side of 1925, but still.) So I kind of feel like I was tricked into reading a book that was really well suited to me. Four stars from me, praise for the author, but not really recommended to most friends or strangers.

[Diego · Rating 4 out of 5]

Me pareció una lectura muy interesante. Es un recorrido a través de los aportes del matemático George Boole y el ingeniero Claude Shannon: el álgebra booleana y su aplicación para el diseño de circuitos digitales respectivamente. Hace un recuento de las aplicaciones de estos aportes: detección y corrección de errores en sistemas de comunicación, el diseño de hardware, la resolución de problemas de lógica, etc. Al final del libro expone sobre computación cuántica, y cómo podría ser usada la lógica booleana en este caso.
No es un libro fácil de leer, a pesar que el autor diga en el prólogo que solo es necesario conocimientos de matemáticas de educación media superior.

[Andy Plonka · Rating 4 out of 5]

As a non mathematician, this book would have worked better for me had I read it versus listened to the audio version. There were lots equations explained which would have been more comprehensible to me if I had seen them written. That being said, George Boole and Claude Shannon certainly made huge contributions to the fields of electronics and engineering.

[Bob · Rating 3 out of 5]

This is a book about logic more than anything else. It seems to be an attempt to introduce readers to the subject material, but I am not so sure this is a good source for someone who wants to learn about propositional calculus, etc. This book may generate a distorted understanding, which would have to be unlearned later.

[Joyita · Rating 2 out of 5]

Not quite what I expected! The content is somewhat bookish (and basic) for electrical engineers. The chapter on quantum computation was slightly more interesting and the language clarifier anecdote in the epilogue mildly amusing.

[Andy Plonka · Rating 4 out of 5]

As an adio book this book is hard for the non mathematician to understand. There are many equations read ti you which would be much more comprehensible if one could see it in print. That said, these two men made great contributions to electronics and engineering which can be appreciated by all.

[Steve Gross · Rating 4 out of 5]

Two chapter-length biographies of George Boole and Claude Shannon, then the rest of the book is devoted to Boolean logic and algebra at a medium level of difficulty. Only for true fans.

[Mills College Library]

510.922 N153 2013

[Dani Ollé · Rating 4 out of 5]

I found unreadable the last chapter on quantum computing but before that the book gives a great insight on Boole's and Shannon's contributions