Impossibility

Man is not a circle with a single center. He is an ellipse with two foci. One is facts. The other is ideas.

-Victor Hugo

Take a good look (Image Courtesy: Wikipedia). The object you are staring at is known as Penrose triangle. And it is an impossible object. Now what do you mean by that? Well, you might already have guessed. The object cannot be constructed. Hence the name. It's just that our brain interprets the image as a projection of a 3 dimensional object. And this is one of the topics dealt with in John Barrow's Impossibility.

Let me start by saying that it was impossible for me to understand some parts of the book :). [But you know my opinion of Mr. Barrow, so you (and I) know whom to blame :p]. As for the rest of the book, it was a delight to read, informative and sometimes illuminating. The subtitle might give an idea of it's contents, The limits of science and the science of limits. It is a rather different kind of popular science book. Generally they focus on what Science has achieved, and tend to give the impression that the march of progress is unstoppable. Here we get to see what kind of constraints to our investigations of nature might exist, along with a look at the history, because the question is clearly not new. They might take many different forms, like limits of economy because information clearly has a cost, limits of technology of how small things can get, limits because the universe is the way it is (like the finite speed of light), limits of our ways of reasoning (those of mathematics), and finally limits of our minds, because we clearly have not evolved to do science, we have evolved to survive and so our minds might have preferences for certain kinds of patterns which may not be ultimately adequate or appropriate for describing the universe. There is an interesting discussion of Arrow's theorem towards the end, which states that under a few reasonable assumptions, it is impossible to rationally convert multiples individual choices (like votes cast by people) into an unambiguous social choice. Another interesting tidbit that I just can not not share is the financial proof of why there are no time travelers (given by Reinganum). Here's how the argument goes. If there are travelers visiting us from the future, they can use their knowledge to make huge profits in futures markets, which will drive the interest rate towards zero. The fact that we see positive interest rates means no time travelers are visiting us. Fundoo.. :)

It took me more than usual amount of time to finish this book, because as I said earlier, I kept getting stuck. But those moments got me thinking about impossibilities on a more mundane, personal level. I mean it's very easy to say Sky is the limit in an exalted moment, but it would be foolish to ignore your limits, if only for the reason that you must identify them before you can transcend them.

Enjoy!!