True Lies

This sentence is false.

The alert reader will be a little perplexed by that claim for if it is true then it must be false, and vice-versa. Statements like this are called paradoxes. This particular paradox is a version of what's called the Liar's Paradox. It's hard to see how a paradox could be true or false and yet it's hard to say exactly what it is that's wrong with the sentence.

There are lots of different kinds of paradoxes. Some are verbal like the one above, some are visual, like the art of M.C. Escher :

And some are situational like the paradoxes of an ancient Greek named Zeno.

Philosopher Graham Priest has an interesting piece at The Opinionator blog on paradoxes and modern attempts to resolve them. It turns out that some people think that though a paradox involves a contradiction some of them are nevertheless true. I have serious reservations about this because it seems to violate a logical principle called the law of non-contradiction which is a bedrock of rational thought. Even so, the article is very interesting, at least for the logically minded, and may even be correct. Give it a look.

Sheer Genius

There's more here on the fascinating story of the Stuxnet virus that infected the computers which run the centrifuges in the Iranian nuclear weapons program. It seems that the people who wrote the code for this cyber weapon thought of just about everything. They must be geniuses which is more than a little scary because there's no reason to think that such a weapon could not be used against us as easily as against the Iranians.

It's not hard to imagine an enemy shutting down our electrical grid, our air traffic control system, our financial system, or our military communications systems with just such a tool. It could be catastrophic, and we wouldn't even know who did it.

Here's an excerpt from the article:

Simply put, Stuxnet is an incredibly advanced, undetectable computer worm that took years to construct and was designed to jump from computer to computer until it found the specific, protected control system that it aimed to destroy: Iran’s nuclear enrichment program.

The target was seemingly impenetrable; for security reasons, it lay several stories underground and was not connected to the World Wide Web. And that meant Stuxnet had to act as sort of a computer cruise missile: As it made its passage through a set of unconnected computers, it had to grow and adapt to security measures and other changes until it reached one that could bring it into the nuclear facility.

When it ultimately found its target, it would have to secretly manipulate it until it was so compromised it ceased normal functions.

And finally, after the job was done, the worm would have to destroy itself without leaving a trace.

That is what we are learning happened at Iran's nuclear facilities -- both at Natanz, which houses the centrifuge arrays used for processing uranium into nuclear fuel, and, to a lesser extent, at Bushehr, Iran's nuclear power plant.

Check out the article at the link.