Home | Amazing | Today | Tags | Publishers | Years | Account | Search 
On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics (The MIT Press)

Buy
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory.


This award-winning book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof.

The book covers Cantor's revolutionary thinking about infinity,
which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.
(HTML tags aren't allowed.)

Digital Electronics: Principles, Devices and Applications
Digital Electronics: Principles, Devices and Applications

Digital electronics is essential to understanding the design and working of a wide range of applications, from consumer and industrial electronics to communications; from embedded systems, and computers to security and military equipment. As the devices used in these applications decrease in size and employ more complex technology, it is...

Digital Photography For Dummies (For Dummies (Computers))
Digital Photography For Dummies (For Dummies (Computers))

Isn’t that digital camera so cool? There must be a hundred things it will do that you haven’t really figured out yet, right? For that matter, just getting the hang of all the features you DO know about may be keeping you busy. With your digital camera, you can

  • See immediately whether you got...
Special Edition Using Visual Basic.NET
Special Edition Using Visual Basic.NET
Microsoft's .NET initiative created drastic changes in the Visual Studio line of products, and as a result a lot of Visual Basic developers feel like they are beginners all over again. Special Edition Using Visual Basic.NET will offer in-depth explorations of new features so that both experienced programmers and novices will feel comfortable making...

The Beginner's Guide to Starting a Garden: 326 Fast, Easy, Affordable Ways to Transform Your Yard One Project at a Time
The Beginner's Guide to Starting a Garden: 326 Fast, Easy, Affordable Ways to Transform Your Yard One Project at a Time
A fresh approach and simple way to transform your yard!
 
The prospect of revamping a yard is daunting. Where do you start? How do all the various areas come together in a beautiful, cohesive way? The Beginner’s Guide to Starting a Garden simplifies the process by showing you how to spend fewer
...
iPhone Game Development (Developer Reference)
iPhone Game Development (Developer Reference)

New Apple Developer Series!

A technical and business guide to creating and selling iPhone games

If you've always wanted to develop a cool iPhone game application and sell it for big bucks, this book is for you. iPhone Game Development covers all technical and commercial bases, from how to sign up...

Blaming Immigrants: Nationalism and the Economics of Global Movement
Blaming Immigrants: Nationalism and the Economics of Global Movement
Immigration is shaking up electoral politics around the world. Anti-immigration and ultranationalistic politics are rising in Europe, the United States, and countries across Asia and Africa. What is causing this nativist fervor? Are immigrants the cause or merely a common scapegoat?

In Blaming Immigrants, economist
...
©2021 LearnIT (support@pdfchm.net) - Privacy Policy