...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"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." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Tuesday, March 6, 2018

"Demented Times," Indeed -- a book review


A book blurb today.... (I mentioned this volume briefly a couple weeks back):



Exact Thinking In Demented Times” is a wonderful title that sounds very apt for current times… but in fact it’s the title of a volume from mathematics professor Karl Sigmund recounting philosophy a century earlier in Europe. The subtitle is: “The Vienna Circle and the Epic Quest for the Foundations of Science.” For any who don’t know, the Vienna Circle was a group of philosophers and scientists who regularly discussed logical positivism and analytical philosophy underlying science (and stood largely in opposition to metaphysics). They included some of the dominant academics and intellectuals of their time.
Like several books I’ve reviewed here over the years, this is more a volume at the fringes of mathematics, than about math itself or doing mathematics. I loved this volume, but one’s enjoyment will hinge on having some inherent interest in the philosophical thought and luminaries that dominated 20th century European philosophy.

This is my first strong book recommendation of 2018, but worth noting it actually came out in the English version toward the end of 2017, and the original German version was even out in 2016. Renowned Douglas Hofstadter wrote the Preface for this edition, and he apparently had much to do with the German-to-English translation as well.

Among the many names that frequent these pages are:

Ludwig Wittgenstein
Bertrand Russell
Kurt Gödel
Karl Popper
Moritz Schlick
Ludwig Boltzmann
Rudolf Carnap
Hans Hahn
Albert Einstein
Friedrich Waismann
Otto Neurath
David Hilbert
Karl Menger

…and many more

I was mainly interested in this volume to read more specifically about the 1) ideas and 2) interactions/personalities of the members of the so-called “Vienna Circle.” The book fulfilled the second of those wishes, but less-so the first. Like other things I’ve read about the Vienna Circle, this volume skirts above the surface of the nitty-gritty philosophical arguments/ideas that resounded back in the day. It may simply be the case that getting down into the weeds of deep philosophical arguments would make for dry, boring reading and is thus voided. The narratives, personalities, and history are what make this a fascinating volume.

The first four chapters (or ~100 pages) are essentially background to the Vienna Circle before the next two chapters really begin discussion about the Circle itself. The next couple chapters veer off again to some elements tangential to the Circle. The second half of the book (my favorite half) returns in large part to a focus on the interactions/clashes/personalities of the Circle members and associates. In total I suspect one third to one half of the volume is concerned with people or history outside the Circle (for example, there is a lot of material on Karl Popper, though he was never an actual member of the Vienna Circle itself).

I more-or-less fathom the fame of Russell, Popper, Gödel, and Carnap, but not as clearly that of some of their contemporaries, and this work doesn’t make some of the other prominent names any more scrutable to me. In particular, I’ve never quite grasped what, beyond a blustery, assertive style, made Ludwig Wittgenstein such a towering figure in 20th century philosophy (interesting, yes, but why so dominating?) — and this volume doesn’t flesh that out any further for me (despite the many pages devoted to him).
Still, overall, this is a highly enjoyable, rich read. 


Finally, I must offer an additional reason to read this historical account — it very much reminds one of the broader events of the world, principally Europe, in the 1930s (and how easily/quickly democratic institutions can be undone in troubled times), which eventually led the world to exclaim in unison, “NEVER again!” A reminder… which today… is very timely.

[Alan Lightman reviewed the volume for the Washington Post here:



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