Tag Archives: bertrand russell

I can understand anything if there’s a comic about it; Logicomix is a comic about logic; therefore, I can understand logic.

…mathematics may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will I hope find comfort in this definition and will probably agree that it is accurate.

-Bertrand Russell from the essay “Mathematics and Metaphysicians”, printed in Mysticism and Logic (London, 1919. Longmans, Green, and Co.), which is in the public domain and is thus freely accessible through Google Books.

To a borderline innumerate person such as myself, the gist of the above quote — that mathematics is in any way unknowable and abstract — is a little shocking. The fundamentals of math that we begin to learn in grade school, and that many of us never really master, seem to be rigid enough. You have little bites of concepts, backed up with practice exercises that a teacher or knowledgeable parent or friend can glance at and determine whether it’s right or wrong. Then you have a test with a small collection of those minor concepts, and you get graded on that. And then you move on to the next set of concepts. Math, from this perspective, is quite knowable. After all, the answers are in the back of the book!

Bertrand Russell, an intellectual superstar of the first half of the 20th century, was driven by the pursuit of certainty, and he is almost certainly referring to himself in the above quote as a person who has been puzzled by the beginnings of mathematics. As a mathematician and logician, Russell relentlessly pursued definitive proof of the most basic concepts. To give an example, he and colleague Alfred North Whitehead famously took 300 pages of dense symbolic text in their influential Principia Mathematica to prove that 1 + 1 = 2. While that might strike many as a world-historic act of navel gazing, it was, in fact, this sort of questioning that led to the establishment of modern logic, without which algorithms and the computers that they run could not have been developed. In a sense, Russell and his peers made this blog possible by laying the conceptual groundwork for computer science.

That quest for finding a rational explanation for everything, and the ultimate impossibility of that task, is a central theme of Logicomix, an ambitious graphic novel by writer Apostolos Doxiadis, computer scientist Christos Papadimitriou, and artists Alecos Papadatos and Annie di Donna. I say ambitious because the authors set out to explain some pretty complex concepts — the sort of math and logic that Russell and Whitehead were working out in the Principia — to a common reader. This is a work of historical fiction, part biography of Russell, part semi-fictional history of science (semi-fictional because most of the events in the book did happen but not exactly as portrayed in the book), and part primer on logic.

To me, the most interesting thing about this book is how the authors set out to accomplish all of that. They do so using a pretty complex technique that involves three main narratives nesting within one another like Russian dolls. They begin the book with the authors in their studio discussing how they will tell this story; this creates the opportunity to explain some of the basic concepts that they will deal with in the Russell narrative, and the authors return to this thread throughout the book when there is a need for explanation or summary of what has happened in the historical narrative. These scenes sort of function like a chorus in a Greek play would.

The next layer features Russell giving a (fictional) speech at an American university at the very outset of World War II. This layer of the story sets us up for a discussion of the question of why we should care about this obscure and complex math — as the world begins to descend into a bloody war, students at the university demand that Russell, who was, in addition to being a mathematician, also a social commentator and a critic of war, take an absolute position against US involvement in the war. Russell’s speech to the students is the third narrative, in which he tells the story of his early life, his work as a young mathematician, and the development of the ideas for which he became famous. Throughout the story of Russell’s life, we return to him making the speech. In this way, we can situate the major theme of his story, that intellectual certainty is hard to come by because every idea is build upon other ideas whose foundation may not be particularly solid, into the real-life context of whether it is wise to take an unambiguous position on a complicated question. Russell ultimately refuses to take a firm stand on the question of whether the US should become involved in World War II, but rather encourages the protesters to think through the problem and come to their own conclusion.

I have been circling around Logicomix for several years. It was first recommended to me by a mathematician friend, who thought it might be a good window for me to get at least a little glimpse into the kind of questions he was grappling with in his research. More recently, my brother, a high school math teacher, told me that he lends his copy of this book to interested students and it often resonates with them. I’m glad that I picked this up when I did, because I happened to be able to consume it in two big gulps, reading on my back patio on two consecutive warm spring evenings. To me, this is the perfect summer read — it’s complex and thought-provoking, but at the same time not so dense as to be too daunting to tackle. Comics are a great way to try to push yourself intellectually; in fact, the “For Beginners” series was an early player in the graphic non-fiction game and have been popular for many years as a not-so-intimidating entree into tough concepts.

For me, however, Logicomix is a much more than just a palatable explanation of difficult philosophical and mathematical concepts. The explanation is there, but it is all in service of the story. Logic is simply another tool that we can use to understand the world around us. When Russell passed away in 1970, the term graphic novel had not yet been coined, and comics were largely considered to be light fare. With Logicomix, authors Doxiadis and Papadimitriou use the medium to beautifully connect history and math to make some powerful points about the nature of the world we live in. I daresay Russell would approve.

-Dan, whose latent interest in math could be an explanation for why I took Algebra I at least three times.

 

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Aspiration: A Very Short Introduction

All right class, raise your hand if you’ve ever had the feeling that you didn’t make the most of the educational opportunities offered to you in your youth. Whether you dropped out or just got an occasional B+ instead of straight A’s, do you ever wonder what could have been if you had just applied yourself a little more?

You’re certainly not alone: a Northwestern study published in 2011 asked a sample of adults to name one regret that really stands out in their memories, and 13% of respondents passed up lost loves, trips not taken, and childhood cruelties to identify a missed educational opportunity as a source of regret. I suspect it’s a common theme among adults — maybe as a kid you spent most of physics class studying the trajectory of a spitball, and now you can’t resist refreshing NASA’s Twitter feed when there’s a big announcement pending. Or perhaps your interest in verse during 7th grade English was limited to finding that just right word to rhyme with “smells” in an ode to your sister, but now you make sure not to miss a reading or 3 Poems By session here at the Library.

Now, we all know there are great pleasures to be found in being a full time student of the People’s University. I’m sure I would have pulled a much better GPA in 10th grade had my schedule resembled my current reading list…

and so forth. (n.b. Obviously pleasure reading and formal schooling are two different things, and I’m sure my dream schedule would be someone else’s [namely, my wife’s] nightmare schedule.)

I think the  dream of a lot of us academic underachievers, however, is that we could somehow suddenly have a broad, traditional, liberal education behind us. Do I want to learn Greek? Um, maybe next year. But do I wish I already knew Greek? Heck yeah!

The publishing industry has long recognized this impulse of wanting to take the easy path to enlightenment. Dr. Eliot‘s prescription at the beginning of the Twentieth Century — 15 minutes a day of hard reading — was supported by a widely-advertised series of books that promised readers the opportunity to become well-educated generalists with just a little effort. The Harvard Classics, and a number of similar publications such as those put out by Library of America, Oxford World Classics, Everyman’s Library, and The Great Courses have long been a great boon for educational late-bloomers as well as people for whom good schooling wasn’t available, offering anybody with access to a library (or some cash to spend on books) the chance to participate in intellectual life that may have otherwise been out of reach.

Even now, in an age in which anyone with access to broadband can sit in on MIT courses, there’s something welcoming about limiting your self-guided education to a book or two on a given topic. After all, it wouldn’t be hard to spend your 15 minutes a day clicking deeper and deeper into a hyperlinked detail in a Wikipedia article, and who needs all of those diversions when there’s a liberal education to be had?

In my opinion, there’s no better resource for the time-pressed aspirational reader than Oxford University Press’ “Very Short Introduction” series. These tiny books — typically between 100 and 150 pages and perfectly sized to fit in the back pocket of a pair of Levis — offer the broadest treatment of the most difficult subjects imaginable, written by top experts for a lay audience.

Imagine if you ran into an CMU professor at a party and, over the course of a drink, she explained her research using analogies, real-life examples, and maybe a quickly drawn graph on a napkin. These are the book version of that.

Very Short Intros

A dabbler’s delight.

There are hundreds of these things, covering topics from Angels to Writing. (I guess they haven’t gotten to X-rays, Yemen, or Zoroastrianism yet.) Some topics seem to better lend themselves to this treatment; I find the natural sciences, psychology, and theology are strengths in this series. But really, I haven’t found a dud in the bunch.  I recently had a good time reading Very Short Introductions to dinosaurs, Bertrand Russell, and the Old Testament. And while I certainly can’t say that I’m now an expert on these subjects, or even have an above-average knowledge of them, I figure that I’ve retained about as much as I would if I had payed attention in school, which is really all I’m after.

Perhaps the American Library Association should have a marketing campaign — “Make up for your misspent youth @ your library!” It has a nice ring to it…

-Dan

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