Well, there's definitely some "utter mathematical illiteracy" going on here. One of the fundamental properties of chaotic systems that, no matter how well characterized the system is, beyond some horizon you cannot predict the exact state the system will be in at a particular point in time - for example, whether a particular summer will be wet or hot and dry.
That doesn't mean that you cannot predict the kinds of behaviour the system will exhibit. You can still predict, for example, that in the long term summers will be hotter and drier. In fact everyone relies on this to some extent - even though it's impossible to predict the weather more than a few days in advance for the same reason, you're still more likely to pack shorts in summer than winter.
The same is true of simple, rigourously analysed chaotic systems like the Lorentz attractor - someone's actually proved that the long-term behaviour of that system is completely stable and will remain that way even in the face of outside noise, but also that even the slightest noise makes it impossible to predict the exact state of the system more than a small amount of time into the future.
That doesn't mean that you cannot predict the kinds of behaviour the system will exhibit. You can still predict, for example, that in the long term summers will be hotter and drier. In fact everyone relies on this to some extent - even though it's impossible to predict the weather more than a few days in advance for the same reason, you're still more likely to pack shorts in summer than winter.
The same is true of simple, rigourously analysed chaotic systems like the Lorentz attractor - someone's actually proved that the long-term behaviour of that system is completely stable and will remain that way even in the face of outside noise, but also that even the slightest noise makes it impossible to predict the exact state of the system more than a small amount of time into the future.