A while ago we had a chat with Mr. Atalay about the interesting fact that you can't express the decimal 0.1 exactly in binary (try it!). I just read a report related to this fact which was the reason of 28 soldiers getting killed in the Gulf War. Excerpt:
"On February 25th, 1991, a Patriot Missile system that had been running for over 100 hours at Dhahran, Saudi Arabia had failed to intercept a SCUD missile. The SCUD hit an Army Barracks, killing 28 Americans. On the next day, the Bug Fix for the system arrived at Dhahran.
The reason this bug occurred is because of a problem with storing time in a 24-bit register. The problem is that time is stored to an accuracy of 1/10th of a second, but a 24-bit register does not have enough precision to store 0.1, so a small fraction of each second is lost. The result is that the register used to keep track of time is off by 0.0001% of the amount of time that the system has been in operation. The problem is that computers do not store information as a standard decimal. Instead, they use binary code, which can not accurately store 1/10th of a second...It was estimated that after running the system for twenty hours, the calculations made using the old algorithm and those made by the new algorithm differed by as much as 1/3 of a second. A SCUD missile can travel more than one mile per second."
Click here and here for other cases of software malfunctions.
By the way, our chat with Mr. Atalay can be summarized as follows:
One aspect of the chaotic systems is that you need an infinite amount of knowledge about the initial conditions of the system to make some prediction (see butterfly effect). Might there be a possibility that with some other form of representation, to solve the difficulty of infinite information requirement? As an example take the decimal 0.1; If we knew only the binary system, we would need an infinite number of digits to represent 0.1 exactly. And if one day a super-intelligent alien visited us and taught us the ultra-high-tech decimal system, voilla, you have exact representation with just 1 significant digit! Of course, instead of adopting this new wisdom, we would quickly proceed to burn that infidel alien (!)
Care to think about Pi and sqrt(2)? Or shall we rather wait for the green guys in flying saucers to drop by?