Godel’s theorem (or at least one of Godel’s theorems) says that no matter what axioms you adopt, there will always be true statements in arithmetic that can’t be proven. In Chapter 10 of The Big Questions I give an explicit example of such a statement, involving Hercules’s ability to win a certain game against a very persistent hydra.

There are many popularizations of Godel’s original argument, of which at least one (by Nagel and Newman) is superb. They do a marvelous job of boiling the argument itself and the surrounding issues down to a little over a hundred sparse pages. But I can boil it down further, into a single blog post. I can do this via the magic of one of my favorite expository techniques, a technique I call “lying”. I will lie to you throughout this post, by sweeping important technical details under the rug and (slightly) corrupting some important ideas to make them easier to grasp—but without, I think, sacrificing the flavor and the gist of the argument. At the end, once we’re clear on the big picture, I’ll ‘fess up to some of those lies.

Here, then, is (more or less) how Godel proved that arithmetic contains true but unprovable statements:

Continue reading ‘Godel in a nutshell’

It seems to be well known that supermarkets charge cereal companies for prime display space. It seems to be less well known that bookstores do the same thing. They do, though. For example, the publisher of The Big Questions is paying for prominent front-of-the-store display space at all Barnes and Noble and Borders stores—except for those located in Manhattan—through the month of November. (At least the B&N contract runs through the end of November; I’m unclear on whether the Borders contract runs as long.)

There have been several reports of individual stores failing to honor this commitment. My publisher will be having a chat about this with the Barnes and Noble folks in a couple of days, and prior to that discussion it would be useful to know just how widespread the problem is.

So—if you happen to be going past a Barnes and Noble (or a Borders) in the next couple of days, I’ll be most grateful to know whether you found The Big Questions out on the front table where it ought to be. You can comment here or email me at “questions at landsburg dot com”. Please include the address of the store, or the street it’s on, or the town it’s in —whatever you’ve got. Thanks for your help!

It’s been a great week on the blog with thoughtful and thought-provoking comments cropping up everywhere. Several threads have touched on the question phrased most succinctly by Al. V. on the Unreasonable Effectiveness of Physics thread:

Are the laws of mathematics inherent in our universe, and therefore really a product of physics (and not the other way around), or are they supra-universal?

This question, of course, plays a starring role in The Big Questions , where I’ve explained why I believe that the supra-universality of mathematics (thanks for that word, Al!) gives the most coherent explanation of why anything exists at all.

Continue reading ‘Another Great Week’