How is this really any different than solving problems utilizing the raw speed of computers? That is, simply enumerating all possibilities of a problem might not really tell you much more than whether there is an answer, either. However, armed with that some folks may be able to find more.

To take your cat example. Now hook up and improve this algorithm in cameras out in the wild and it will become much easier to track where cats are found. Want a rough count of the unique stray cats in an area? Is there a camera that covers it? :)

That is to say, sometimes we simply need the data that these algorithms can provide in order to feed other decisions. This is really no different than any other situation where you have to infer a wider truth from limited data. We are just expanding our ability to do so, now. Not necessarily by finding the fundamental equation to something, but by applying simpler equations to more and more data. Right?