There's a lot of other fun stuff as well, but it's the Gödel proof that's the core of the book, and if that doesn't turn you on then you aren't really going to think GEB is worth the effort. This is a nice book if you want to understand the Gödel incompleteness proof, and get an account that is both accessible and reasonably rigorous. Join my 3-emails-a-year newsletter #prizes
However, even without taking pen to paper and labouring through the instructive exercises you can get a pretty decent glimpse at some exciting and fundamental thinking. Godel shows us that (I paraphrase drastically) that all logical systems allow statements about natural numbers that are true but unprovable within the system.Īnd somehow this isn't even what the book's about.Īs the pages turn you will be steadily more tested and at some point it will become apparent you've not been paying close enough attention. If you let him Hofstadter will show you how Godel destroyed Betrand Russell's Principa Mathematica - his attempt to logically deduce all of mathematics from a set of axioms. Number theory requires no great resource of mathematical knowledge - just an extremely agile and open mind. I seem to remember Achilles spends a lot of time talking to a tortoise. Hofstadter makes some fascinating observations about emergent properties (such as intelligence) and diverts us into the extremely heavy mathematics of Godel via the self referencing systems that are Bach's fugues and Escher's 'optical illusion' style artwork.īefore too many chapters have passed though you'll be firmly in number theory land, albeit doled out as painlessly as is possible with such stuff, leavened with imagined philosophical debates between ancient Greeks and other proxies. Before too many chapters have passed though you'll be firmly in number theory land, albeit doled out as painlessly as is possible with such stuff, leavened with imagined phi Expand your mind! Not for the faint of heart & yet by no means dry. Hofstadter makes some fascinating observations about emergent properties (such as intelligence) and diverts us into the extremely heavy mathematics of Godel via the self referencing systems that are Bach's fugues and Escher's 'optical illusion' style artwork. Expand your mind! Not for the faint of heart & yet by no means dry.
0 kommentar(er)
