Review When Einstein Walked with Gödel

Math and philosophy have always been two sides of the same coin to me. One uses numbers and symbols to build logical arguments, and the other uses words as its tools. While the goals look different, they are actually very similar. Both disciplines seek to explain the beauty of the world they observe around them, and let’s face it, popular culture views the practitioners of both as intelligent ascetic scholars locked in their academic towers living lives wholly of the mind writing and creating papers for other scholars. But there exists certain scholars who wish to bridge the gap between those inside and outside the academic disciplines. When Einstein Walked with Gödel: Excursions to the Edge of Thought by Jim Holt from Farrar, Straus, & Giroux seeks to bring a philosopher’s gaze to the discipline of mathematics, and he largely succeeds. This collection of previously published essays paints a picture of a careful writer wrestling with the mathematician’s place in history. Mr. Holt writes with authority over a wide range of ideas, and he’s found the right balance of challenging and accessibility. When Einstein Walked with Gödel is an excellent addition to my growing list of scientific, mathematical, and philosophical publications; recommended for anyone who wants a survey of the deep ideas in those fields.

TL;DR

Well-written, thoroughly researched and argued collection of essays wrestling with the difficult topics of mathematics. Recommended for anyone who wants an accessible but challenging look at some of humanity’s deepest problems. This book will make you think.

From the Publisher

From Jim Holt, the New York Times bestselling author of Why Does the World Exist?, comes an entertaining and accessible guide to the most profound scientific and mathematical ideas of recent centuries in When Einstein Walked with Gödel: Excursions to the Edge of Thought.

Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction—and whether the universe truly has a future.

Walking with Big Ideas

From infinity to string theory to Mandelbrot to the Riemann Zeta conjecture, Mr. Holt covers the big ideas of mathematics. The essays approach these ideas from a descriptive rather than technical standpoint, and many have a historical and biographical focus that place the mathematical concept in time. To organize the book, essays are grouped into nine sections. Part eight consists of shorter, quicker essays that are unique to this book. Overall, the book covers a lot of ground but doesn’t just skim. Mr. Holt dives into the ideas to produce thorough and enlightening work.

Writing

Receiving an Advanced Reader Copy (ARC) of When Einstein Walked with Gödel made me ridiculously happy. It hits two of my favorite areas of reading, philosophy and math, but it does so in a pragmatic way. When I pick up scientific/philosophy books, I’m looking for the middle ground of being understandable without being condescending or written with too much hand-holding. Collections like this should be – as it says in the description – accessible. What does accessible mean, though? To me, an accessible scholarly work means that a deep knowledge is not necessary, but the text still requires intellectual interaction. When Einstein Walked with Gödel hits this sweet spot of shining light on tough ideas while not being out of my intellectual capabilities. Mr. Holt accomplishes this through a mix of translating academic ideas from math to practical descriptions, biography, history, and book reviews. It’s clear that Mr. Holt does exhaustive research for his articles and thinks deeply about each topic. With any scientific work, the writing determines the success of the book, and Mr. Holt’s writing is excellent, challenging, and precise. In nearly every essay, Mr. Holt slips easily into a very high diction that had me running to the dictionary; he loved slipping in $100 words or haughty phrases. These moments felt self-congratulatory and knocked me out of the essay but each occurrence was momentary.

The Problem with Collections

As this is a collection of essays and not one whole work, each section provides a new topic, a new argument. Like any collection, some work better than others. The titular essay and Truth and Reference: A Philosophical Feud stood out as the two best. The three essays dealing with the mathematical concept of infinity, and, in particular, The Dangerous Idea of the Infinitesimal, shifted my perspective on the slippery concept in an entertaining way. Mr. Holt’s shorter essays mostly succeeded as more philosophical sketches than essays. Though I think of them more as intellectual snacks when compared to the full meals that are his essays, these short pieces will make you think, or, at least, say “aha.” Overall, When Einstein Walked with Gödel avoids the problem with collection by being filled with many strong pieces. While there were a few weaker essays, only one stood out as a real negative.

Poor Ada Lovelace

In the The Ada Perplex, Jim Holt questions whether Byron’s daughter deserves the historical position that she occupies, and the well-researched essay casts doubt on her position. But I can’t help notice that the reasons used by Mr. Holt align with historical methods of erasing the contributions of women. Hell, just the cover of Joanna Russ’s How to Suppress Women’s Writing lists examples of the arguments that Mr. Holt used to show that Ada may not deserve her vaunted place. Even upon finishing the whole collection, I still don’t know what to make of the Ada Lovelace essay because her contributions are debated but not erased. While this essay attempts to walk the thin line between shedding light on a necessary debate and controversy, I don’t think it succeeds. Her collaboration with Babbage should be scrutinized, but she shouldn’t be discounted as a contributor. Mr. Holt, clearly, researched the hell out of this topic, and if he found obvious evidence for his conclusion, it wasn’t effectively argued in his essay. In the later essay Truth and Reference: A Philosophical Feud, Mr. Holt succeeds in clearly laying out a controversy without erasing Ruth Barcan Marcus’s contributions, which shows he possesses the capability to write about a difficult topic without erasure. It could be that the second essay succeeds where the first doesn’t because of historical distance between the two events. I just wish he’d handled Ada’s case with a little more care.

Gödel

Gödel and his incompleteness theorem pop up frequently throughout this collection. Whether a byproduct of research, personal bias, or just being right there on his mind, Mr. Holt slips Kurt Gödel into many of the essays. While noticeable, the reference never feels forced. Much the same way a physicist drops Einstein or Feynman into conversation, Mr. Holt name-checks Gödel. All of these references indicate where Mr. Holt places the Austrian in the pantheon of great mathematicians. Simply because of Mr. Holt’s his intellectual rigor and repeated usage of Gödel throughout the collection, he made me curious to learn more about the mathematician and his incompleteness theorem, which is currently beyond my grasp, not that I’ve spent much time on it. However, this is one of the things I enjoyed about the book because it places Mr. Holt in an intellectual lineage. Before this collection, I knew little of Kurt Gödel other than he had an important theorem. Now, I owe Mr. Holt a debt for piquing my curiosity about this strange genius.

Conclusion

When Einstein Walked with Gödel: Excursions to the Edge of Thought exceeded my expectations all around. While some essays missed and one failed, overall the collection presents an enticing, in-depth look at big ideas, maybe some of the biggest ideas in human intellectual history. This accessible yet challenging book educated me on every page without boring me. The very best essays stuck with me long after I finished reading them, and I realized it was because Jim Holt had taken exceedingly complex ideas and distilled them down to their essences. In When Einstein Walked with Gödel: Excursions to the Edge of Thought, Jim Holt translated academic beauty into the layperson’s splendor.

8 out of 10