Infinity and the Mind

Rudy Rucker, son of a cleric and mathematics whiz kid, produced this book on `Infinity and the Mind' years ago, but reading and re-reading it, I continue to get insights and the chance to wrap my mind around strange concepts. `This book discusses every kind of infinity: potential and actual, mathematical and physical, theological and mundane. Talking about infinity leads to many fascinating paradoxes. By closely examining these paradoxes we learn a great deal about the human mind, its powers, and its limitations.'This book was intended to be accessible by those without graduate-level education in mathematics (i.e., most of us) while still being of interest to those even at the highest levels of mathematical expertise. Even if the goal of infinity is never reached, there is value in the journey. Rucker provides a short overview of the history of 'infinity' thinking; how one thinks about divinity is closely related often, and how one thinks about mathematical and cosmological to-the-point-of-absurdities comes into play here. Quite often infinite thinking becomes circular thinking: Aquinas's Aristotelian thinking demonstrates the circularity in asking if an infinitely powerful God can make an infinitely powerful thing; can he make an unmade thing? (Of course, we must ask the grammatical and logical questions here--does this even make sense?)Rucker explores physical infinities, spatial infinities, numerical infinities, and more. There are infinites of the large (the universe, and beyond?), infinities of the small (what is the smallest number you can think of, then take half, then take half, then take half...), infinities that are nonetheless limited (the number of divisions of a single glass of water can be infinite, yet never exceed the volume of water in the glass), and finally the Absolute.`In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible.'At the end of each chapter, Rucker provides puzzles and paradoxes to tantalise and confuse. * Consider a very durable ceiling lamp that has an on-off pull string. Say the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?Rucker explores the philosophical points of infinity with wit and care. He explores the ideas behind and implications of Gödel's Incompleteness Theorem, and leads discussion and excursion into self-referential problems and set theory problems and solutions.He also discusses, contrary to conventional wisdom, the non-mechanisability of mathematics. We tend to think in our day that mathematics is the one mechanical-prone discipline, unlike poetry or creative arts and more 'human' endeavours. But Rucker discusses the problems of situations which require decision-making and discernment in mathematical choices that no machin

I know very little about any of the subjects discussed in this book, although I do have a degree in philosophy of science, and I liked this book a lot. I can't believe I made it through 7 years of senior school and 2 years of degree level maths and nobody ever bothered to tell me about infinity, transfinite numbers, set theory and its relationships with, and underpinning of other branches of mathematics in a way I could understand rather than simply regurgitate. Rucker on the other hand manages to do this in 362 pages. I slso found the stuff about Godel and the impossibility of complete formulisms very useful, not only philosophically, but also just for my own peace of mind.

In many ways, infinity is the most abstract concept of all. Many of the advances in understanding how to manipulate infinities had unpleasant consequences. As the legend goes, the first one to announce that there are infinite non-repeating decimals was rewarded by being drowned. Georg Cantor, the first to prove that there are different levels of infinity, faced extreme criticism and ultimately went mad. Fortunately, Rudy Rucker provides a gentle introduction to this concept, one that can be read by most with the only consequence being enlightenment. The entire range of infinities (what a phrase!) is covered in this book. From the simplest infinity (omega), to the multi-universe theories of quantum theory. All are put forward in a very readable style, although there are times when one must slow down and read very carefully if one is to understand. Rucker's encounters with Kurt Godel is a welcome contrast with the common depiction that he was a dry, humorless man. It is refreshing to hear that he laughed and had a sense of humor. Many different test scenarios have been put forward to determine if a computer is indeed intelligent. At this time, I would propose that any machine that can understand the concept of infinity must be considered intelligent. Any human wishing to pass that test need only read this book. It should be required reading in all undergraduate mathematics programs. Published in Journal of Recreational Mathematics, reprinted with permission.

Not an easy read. Compare it to training for a marathon, not fun at first but a new perspective of being evolves. It has taken me a good six months to read and reread and still parts I am shady on. I still am not totally finished with this book but recommend it.

Yeah, its a book on math and a book on philosophy. Actually, it's a bit more. It's a book that uses mathematics as an approach to philosophy, but certainly not in a mechanist or reductionist fashion; after all, what's the last book by a mathematician that treated mysticism as a serious philosophy? Inside you learn about: what sorts of infinity there might be, why the ancients and medievals were uncomfortable with infinity, truth, randomness, transfinite arithmetic, Hilbert's Hotel, robots and souls, and quite a bit more. Bottom line-the mathematical discussions can be tough slogging at times, but are explained thoroughly and in fine detail, with wit and charm, and the whole constitutes one of the richest scource of ideas I have ever come across. A bargain at twice the price!