Two Volumes….

My favorite form of writing (to read) is the essay. Books on single themes, no matter how well-written, invariably lapse into sections or passages that are redundant, plodding, or pedantic. The essay form is brief enough to be rich and scintillating from beginning to end, in the hands of a good craftsman. 

All this to say, that even though it’s only June I think I have already found my favorite book-of-the-year in Jim Holt’s “When Einstein Walked with Gödel,” a compendium of 20-years-worth of Holt essays. I don’t expect anything I see the rest of the year (though I could be wrong) to surpass the joy I’m getting from these beautiful pieces on physics, philosophy, culture, and abundant math. At 3/4 of the way through there hasn’t been a bad, boring, or weak essay yet, nor expected in the final 1/4. I’ve been marking my very favorite essays as I go along, but so many are now thusly-marked it’s not even worth noting them all. Wonderful descriptions of and anecdotes about great figures in the history of math/science; wonderful discussion of debates/controversies in the scientific/philosophical realm; wonderful, thought-provoking, often novel, commentaries and overviews. I’ve already touted this volume in various places, and can’t recommend it enough; readable and enjoyable by professionals and laypersons alike. 

Here are some more formal review links:

https://bookmarks.reviews/reviews/when-einstein-walked-with-godel-excursions-to-the-edge-of-thought/

…and also a review and interview with Holt here:

https://medium.com/@ja.alper20/when-einstein-walked-with-godel-3431e2349ef6

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Received an uncorrected review copy of Eugenia Cheng’s forthcoming (September?), “The Art of Logic In an Illogical World” awhile back. It’s Dr. Cheng’s third book and again an attempt to present somewhat abstract topics (previously category theory and infinity) to a general audience. Oddly, in each instance I’ve enjoyed one half of each of her books better than the other half; in this case it was the second half I enjoyed most — I won’t dwell on that, since your ‘mileage may vary,’ but mention it just so you know that if the first half doesn’t grab you, persevere, and the second half may be more rewarding.

Dr. Cheng’s topic this go-around is very timely and important, as it has to do with how people think, reason, form opinions, argue, etc. in this highly-polarized world we inhabit. Important to note that there is very little technical logic/symbolism in the volume, even when she is discussing elements of formal logic. Her tone/presentation is much more informal/casual, almost conversational — that has always been her writing style as she strives to reach a broad audience. In fact I would almost say that the title of the book could equally well be “The Art of Common Sense” because she is dealing with logic in such an informal, introductory way that it will often seem like just formalized common sense.

One of the main strengths of the book is that she employs very current issues or examples (often related to equality or feminism)  to illustrate her points throughout, making what could have been abstract or stodgy material, rather more pertinent and interesting.

Early in the book Dr. Cheng notes that she has sometimes been described as “pedantic” for her previous writing, and I think that is a fair warning of how some will view passages here as well (again, more-so the first half of the book). But then she consistently takes on subjects (like category theory, infinity, and now logic) that lend themselves to pedantry (despite her constant attempt at casualness… which I find a bit annoying at times, but may well appeal to her intended audience).

Dr. Cheng’s enthusiasm for her topics is unmistakeable; she already has a large fan-base and 3 books (and many articles and videos) under her belt — each of those volumes are good, but I suspect the most excellent works from this energetic, relatively young writer are yet to come, as she endeavors to spread the good news of mathematics AND logical thinking far and wide.

From Whence...?

"The more the universe seems comprehensible the more it also seems pointless."
-- physicist Steven Weinberg as famously quoted in Jim Holt's "Why Does the World Exist?"


I'm currently finishing Jim Holt's bestseller (and one of the NY Times' Top 10 nonfiction picks for 2012), "Why Does the World Exist?" (now out in paperback). Won't write a full review since it's more philosophy than math or science, but will recommend it to those with a philosophical bent, or who have enjoyed any of the other recent books on that most fundamental of questions, 'why is there something instead of nothing?"

The first half of Holt's book, while good, takes a little bit of time to gain traction, and the second half is especially good and invigorating. Holt keeps the sometimes deep philosophical and theoretical discussion not only accessible, but also moving along at a pace which doesn't get too bogged down with any one set of arguments or thinker. If you are someone who scoffs at the very idea of reading an entire book on a question that essentially can't be answered, then you'll want to pass on this volume, but if you enjoy seeing the wide variety of cerebral exercises major thinkers have employed to approach this basic conundrum than Holt takes you on a good ride, tossing in personal anecdotes along the way.

My favorite chapter (not too surprisingly) is chapter 10 on Platonism, where, in addition to Plato, the likes of Kurt Gödel, Roger Penrose, Max Tegmark, Bertrand Russell, and Hartry Field are among those making appearances in the debate over whether there is an independent platonic realm of mathematics (apart from human consciousness), or is mathematics merely a human construction. Both sides have very astute and brilliant proponents.

The mini-portraits of the many fascinating individuals Holt discusses or holds court with in this book are just as interesting as the ideas they put forth. John Updike fans will find a chapter toward the end (#13) with their literary hero. Heidegger, Quine, Wittgenstein, Leibniz, Richard Swinburne, David Deutsch, Adolf Grunbaum, Derek Parfit, John Leslie, Thomas Nagel, Robert Nozick, are among the intriguing panoply of players (living and dead) who are aired in these pages (many individuals who I was not previously familiar with at all).  Some of the book's philosophical discussion is a bit muddied in semantics (as could be expected), and I prefer the discussions with scientists, but Holt deftly works his way through all of it, be it religion, cosmology, or quantum mechanics. And at the end comes a moving chapter on the death of his own mother.

For some extended reviews of the book here are two (of several) from the Web:

http://bnreview.barnesandnoble.com/t5/Reviews-Essays/Why-Does-the-World-Exist/ba-p/8475

http://articles.washingtonpost.com/2013-02-08/opinions/36990295_1_wrong-question-answer-universe

Of course the volume reaches no final resolution and there is a bit of predictability in so much as certain issues keep recurring as sticking points, yet the intellectual exercise remains entertaining. Holt notes early on in the volume that the question of why the world exists is "so simple that it would occur only to a child." Maybe that explains why, despite its intractability,  we find it such an irresistible inquiry... it makes us all feel like children again in this great big farfetched universe of ours (...or, multiverse).

One last thing:
The quotation I've long-used from Bertrand Russell heading my Math-Frolic blog comes from early in his career when his optimism about mathematics and empiricism was strong. Holt's book (again the chapter on Platonism) introduced me to another quote, I was unfamiliar with, from much later in Russell's storied life. I love the quote, and change-of-heart it expresses, so much so that I've added it to the Math-Frolic blog heading, and will leave you with it here:

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal."

[NOTE: I've actually since moved the paired quotes over to the MathTango heading.]

[...This all reminds me of yet another brand new book now showing up in bookstores: not meaning to stray too far from mathematics, but computer scientist/keen-thinker Douglas Hofstadter's latest tome is, "Surfaces and Essences" (about the role of 'analogy' in human cognition), and I suspect it is must-reading for anyone interested in cognition. (Hofstadter was author of "Gödel, Escher, Bach," one of the most acclaimed works of nonfiction of the last half-century, and several works since. He also took over Martin Gardner's column at Scientific American for a few years back when Gardner retired.)]