One of my pet peeves is the belief that "creative" people are those who study the humanities and that "analytical" types (as if "analytical" must someOne of my pet peeves is the belief that "creative" people are those who study the humanities and that "analytical" types (as if "analytical" must somehow stand in opposition to creativity) are those who study sciences and mathematics. Perhaps this belief stems from a mathematics education grounded in rote, memorization, and dull exercises. The Mathematical Experience is about mathematics, but takes a much more philosophical tone, exploring the concept of proof and truth, the history of math, and the process of discovery/invention of new ideas and theorems. I enjoyed it very much.
The book takes the form of several essays, averaging a few pages long each. I particularly enjoyed:
- "Unorthodoxies," about crank ideas but also the possibility of valuable ideas appearing to be cranks at first. "The doors of the mathematical past are often rusted. If an inner chamber is difficult of access, it does not necessarily mean there is treasure to be found therein."
- The chapter on the Chinese Remainder Theorem, a really fantastic survey of the same idea as seen through different mathematical lenses over history.
- "Nonstandard Analysis" was a thought-provoking essay about the history of the infinitesimal dx - like most present-day people I had learned it as expressed in terms of limits (the Weierstrassian "reformation," as it were) but had no idea of the infinitesimal's controversial use in other proofs. Challenges the concept of rigor, as practically useful results were "proved" in non-rigorous ways; of what use, and how much use, is rigor, and what is the role of intuition? (This was a far better exploration of the topic than the chapter devoted explicitly to intuition.)
- The essays towards the end hammer a little over-long on the distinctions between Platonism (mathematics is universal, immutable truth "out there" that we discover), constructivism (we invent mathematics, and objects must be constructed for their existence to be proved), and formalism (math is just a set of rule manipulations that does not encompass philosophical questions). But I did find the initial discussion of it to be very interesting.
- The two computer-oriented essays, "Mathematical Models, Computers, and Platonism," and "Why Should I Believe a Computer?" I think it would be wonderful if a mathematician with writing talents would update this book with more about how computers have influenced the development of mathematics. ...more
A really thought-provoking collection of essays and short stories about sentience. Each essay or story is followed by a short discussion by HofstadterA really thought-provoking collection of essays and short stories about sentience. Each essay or story is followed by a short discussion by Hofstadter and/or Dennett. I enjoyed most of them, and even the ones I didn't particularly enjoy still added fresh perspective that I appreciated. Some great mind-benders in here.
The two stories by Stanislaw Lem, "The Seventh Sally" and "Non Serviam," are superb; I'd never read Lem before but I'm certainly going to be putting him on my reading lists. "The Seventh Sally" was an inspiration for SimCity. Harold Morowitz's "Rediscovering the Mind" is a great comparison of the role of an "observer" in quantum physics with the increasing reductionism in biology that leaves no place for consciousness. Jorge Luis Borges and Richard Dawkins are two of my favorite authors and this book includes two stories by Borges and a selection from Dawkins's excellent The Selfish Gene. John Searle's famous "Minds, Brains, and Programs" describes his famous "Chinese room" thought experiment and offers a lot to think and argue about. The introduction, written by Dennett, is also very good. ...more
This edition of Machiavelli, published by Barnes & Noble, includes The Prince in its entirety, two letters to friends, and excerpts from The DiscoThis edition of Machiavelli, published by Barnes & Noble, includes The Prince in its entirety, two letters to friends, and excerpts from The Discourses. The Prince, naturally, takes center stage. I think of Sun Tzu's The Art of War as the stereotypical businessman's nod to the classics, but I found this to be more enjoyable and relevant. It feels provokingly sensible even today, almost 500 years after it was originally written, to anyone whose job involves managing people and vying with rivals for superiority.
Some describe Machiavelli's philosophy as "the end justifies the means," which is accurate at times. But I think a fairer assessment of him is that he is a realist with a dim view of human nature. The term realpolitik comes to mind. The Prince is not about justifying whatever goal you want to achieve, but specifically about gaining and maintaining power and sovereignty and acknowledging that this can involve deception and suspensions of traditional morality.
I particularly recommend the sections on avoiding contempt and hatred, which Machiavelli says, and I agree, is a fatal flaw for a prince. (And wherever you see "prince" or a similar term you can read "manager" for our modern workplace.) A ruler has to show strength but in a balanced way, as too little or too much will make him despised by his people. I also recommend the first few chapters, regarding hereditary princes versus princes who obtain power by conquest; while this sounds on first glance like it would have aged poorly, I found that it analogized well to workplaces where a manager is promoted from within versus where she is hired from elsewhere.
The first of Machiavelli's letters, "The Life of Castruccio," espouses a similar philosophy to The Prince but isn't as well written. The second letter, to Francesco Vettori, is very short and is more of a historical supplement. The excerpts from The Discourses also are similar in nature to The Prince but are better than "Castruccio" and provide some sharp observations on the role of religion and traditions. (Make a show of obeying them even if you don't believe them, as they instill order and confidence.)
The introduction and endnotes, supplied by Prof. Wayne Rebhorn at UT, are clear and offer the reader the depth of understanding that you'd want to see out of all ancillary material. Rebhorn emphasizes historical context, describing the wars and politics and rulers of Europe in the 1400s and 1500s and how they shaped Machiavelli's life and thoughts. ...more
I picked this up because somewhere along the way I was told that you absolutely had to read this book to understand European Middle Ages literature anI picked this up because somewhere along the way I was told that you absolutely had to read this book to understand European Middle Ages literature and way of thinking. I think that it is strictly in this context that you have to appreciate this book: examining how it shaped other thinkers and learning historical concepts in philosophy without actually taking the ideas at face value. Because honestly as a work of logic, as something in which you'd try to find truth or real understanding about the world, it's pretty bad.
The book imagines a dialogue with a muse-like spirit Philosophy who communes with Boethius, the author and narrator, as he sits in prison. The chapters consists of prose alternated with poetry; I found the latter to be much more enjoyable, and I liked the effect of the alternation on how I read and digested the content. As it is helpful for a textbook to periodically recap its material, so it was helpful, not to mention artistically stylish, to finish chapters with poems covering the same concepts.
The prose generally consists of Philosophy making sometimes winding statements that purport to be logically built upon one another but are not always so, with Boethius only very rarely objecting and most of the time replying with a dumb agreement. In a muddling of reason Philosophy unconvincingly entangles the concept of goodness with power, wholeness, self-sufficiency, and happiness, claiming their equivalence and then uses this shaky ground as a foundation for other claims. Later on the book, with regard to theodicy, falls back on one of the worst, tritest old saws out there, that it's all part of God's plan and that as humans we just wouldn't understand. The latter half of the book perambulates uselessly around these two ideas and is pretty much all poor.
I did find the first half of the book better, enjoying the discussion about what in life makes people happy and why none alone are sufficient to truly satisfy. I also enjoyed one passage at the end where Philosophy describes God's perception of the world as simultaneous, perceiving future and past concurrently as if time were a spatial dimension. This conception of God I found to be very advanced and sophisticated, particularly given that it was written 1500 years ago. And I also liked seeing the theme of anamnesis weave in and out of the pages. The introduction in the Penguin edition, which was very educational though a little obsequious towards Boethius, mentions this concept, which is the treatment of human knowledge as a recollection of things forgotten as opposed to learning something genuinely new, and often times you can see Boethius touch back on this in his writing.
But, as I mentioned at the outset, I found these interesting not as actual ideas I would take seriously in real life but as concepts that have shaped the later growth of human intellect. Anamnesis to me is a potentially neat literary device, but nothing more. And for me it's hard to rate a book very highly, even from a strictly historical lens, if it presents itself as a book of truths but is so suspect in its reasoning and derivations. ...more
Like much of this book's target audience, I am only familiar with the Bible to the extent that it was taught as a religious text in church. (I went toLike much of this book's target audience, I am only familiar with the Bible to the extent that it was taught as a religious text in church. (I went to church when younger but am not religious at all now.) Therefore it's hard for me to judge whether this book is necessarily a good introduction into biblical scholarship, as I am not familiar with the field in general, any opposing schools of thought, or any debate regarding the merits of the evidence used in the writing.
That having been said, Who Wrote the Bible is informative and engaging. "The Bible" here refers specifically to the books of the Torah, Genesis through Deuteronomy, with shorter mentions to a few others, all in the Old Testament. The author, Richard Friedman, depicts the Torah as the stitched and edited product of several other works written many years apart, each of which was influenced by its author's time and place in the history of ancient Israel and Judah.
Sometimes the evidence feels a bit stretched and speculative, particularly when offering up potential authorial motives; Friedman sometimes obviates the problems associated with this tack by offering many of them that perhaps don't mean as much individually but are harder to ignore when combined. This sometimes works and sometimes doesn't. For example, I think this is effective in the section discussing the person who he thinks combined the Torah into its final form, but not as much when discussing the "D" source. Even when not entirely convincing, the book is thought-provoking, which I appreciate, and it certainly wasn't shy about presenting theories.
Although this may be less appealing to a purely popular audience, I wish he had gone over some of the more objective analyses and evidence in greater depth. For example, I would like to know more about lexical studies of ancient languages and how different grammatical forms have been used to pick out different authors, and also more about archaeological finds. (I thought the scroll seal was really neat but unfortunately it's discussed for all of two pages.) Being unfamiliar with the details of the evidence, I sort of have to take whatever Friedman says at face value; having him step through those details, particularly the less interpretive and more scientific pieces, would have really helped.
Still, the book taught me a lot about what modern scholars know about the Bible (but not really modern scholars; this book is over 20 years old now) and was fun to read. And it did a nice job weaving the reader between the printed word and the context of history. ...more
Before reading this, I'd heard it often described as a book discussing the similarities between music, art, and math. I've since found that to be a faBefore reading this, I'd heard it often described as a book discussing the similarities between music, art, and math. I've since found that to be a fairly incomplete (!) description; it's really more about the theme of self-reference and how it is manifested in those three disciplines as well as other areas, such as biology and artificial intelligence. The latter is particularly important, as Hofstader's "greater idea" here is that the concept of self-reference goes a long way towards the idea of consciousness and uniting the concepts of free will and determinism.
The book alternates between chapters that directly discuss self-reference like a "normal" book and short fictional dialogues between characters Achilles, the Tortoise, and some other friends (including, at one point, the author himself). The dialogues are slam-bang amazing, constituting some of the most delightful and witty writing that I have ever had the pleasure of reading. The rest of the book, its "meat," is still excellent, although I think it could have been shortened. Occasionally Hofstader stretches too much to draw his links between his disparate subjects. But there is a lot of terrifically fertile intellectual ground to tread upon here. (You might even say that the grounds are excellent!)
The size of the book and the fact that it directly uses formalized mathematics (although with as gentle a touch as possible for the general audience) may make this a daunting book to read. I recommend it for everyone though, particularly those without pre-existing backgrounds in logic/CS/math, as its ideas are too important, and its presentation too well-done, to pass it by. ...more