Loren R. Graham

Leerde meer over het begrip oneindigheid. De auteur maakt een goede onderbouwing dat de Russische wiskundigen met het begrip 'oneindigheid' om konden gaan door hun mystieke geloof, beter dan hun Franse collega's die oneindigheid als iets niet rationeel, onbegrijpelijk beschouwden.
De gruwelijkheden van het communisme komen er in voor, en hoe ieder van hun daar mee omgingen.
Enige minpunt vond ik het gebrek aan wiskundige formules. Ik kan me voorstellen dat veel redacteurs daar een streep doorzetten, maar in een boek over geschiedenis van wiskunde mag een formule niet ontbreken.… (más)

From at least the days of the ancient Greek philosophers, mathematical and philosophical inquiry has gone hand in hand, especially where the infinite is involved. And infinities have always involved paradox. For instance, Zeno gave us the example of a fast runner trying to catch a tortoise. First the runner gets halfway to the tortoise, then gets halfway from that point to the tortoise, and so on. The runner can never catch the tortoise because he must make an infinite number of these "half-steps" to get to the tortoise. And yet in real life, runners catch tortoises quite easily. Trying to understand the nature of reality is a major effort in mathematical research - and set theory was developed in part to try to answer these questions. Georg Cantor developed an approach to explore the nature of mathematical infinities that was extended by the French mathematical community, but the reality-based nature of the French approach to mathematics prevented them from getting to what we would consider modern set theory. The French approach to philosophical thinking in the late 19th and early 20th century also struggled with the nature of the infinite in consistent ways; is infinity an ideal or can an infinity be made actual?

But in Moscow, a small group of young mathematicians discovered Cantor's work and came at it from an approach informed by their religious thinking. All were strongly aligned with the Russian Orthodox Church and a mystical approach known as "Name Worship" (sometimes even considered heretical by the church hierarchy). Name Worshipers recite prayers that recognize the names of God, and they consider that the prayers by naming God in some sense bring God into actuality. This difference in outlook from the French mathematical community led this group that became the Moscow School of Mathematics to develop descriptive set theory, an early version of modern set theory.

Naming Infinity is a nicely done history of this process of mathematical research. The set theory and Cantor's approach to infinities is well described at a level appropriate for a general audience. But the majority of the book isn't about the math. It's about the people doing the math. These are some fascinating people who lived through some difficult times, especially after the Soviet Union was established and through Stalin's reign. It's the story of competition between mathematical communities, between individuals within the Moscow School and the Soviet system, even between the Soviet government and the Russian Orthodox Church. It's a short book - about 200 pages of text - but there's a great history in it.… (más)

The Ghost is nominally about an engineer named Peter Palchinsky. Apparently Peter Palchinsky was all for revolution, but demanded that manufacturing and construction needed to take the human element of the worker into account, and that things should be designed before being built. (It's interesting that one of the repeated complaints I've read from computer programmers is that their bosses want them to skip the design phase and start coding immediately.) Apparently he was a good enough engineer to survive not only the Tsar but Lenin and the early Bolshevik days (he wasn't a huge fan of the Bolsheviks) but then ran into Stalin with a complete lack of the political sensibilities that would allow him to survive such an encounter. The author ties this into several of the engineering projects, like the White Sea Canal, where Stalin threw man-power and human lives (100,000, by some estimates) to produce as fast as possible a canal that has always been nearly completely useless.

I'm skeptical of some of the connections drawn here, but the heart of the book is in the biography and engineering stories, and they do shine through. Some mind-boggling facts jump out; in 1986, most of the members of the Politburo had engineering educations, but engineers had to take 3 non-technical classes: political economy (i.e. the Marxist stages of history), dialectic materialism, and the history of the Communist Party. I do feel that more explanation would have been useful about why so few people were interested in studying engineering, if it was the road to political power it seemed to be.… (más)