actually it's closer than you might think. If you consider the eye and visual cortex to be the first layers of a deep learning network, we are actually getting a relatively similar system. However it has limitations further down the line in information representation stuff. The eye is genetically programmed to detect lines, hard edges, colours, and more complex patterns. This is exactly the same as the first layers of a neural net.

However we then humanly assemble stuff like cat = eyes+fur+pointy+cute+small+meowing. A neural net has no way yet to represent information at that level, but we are getting closer there than going beyond dumb numbers. A neural net has implicitly the concept, but is not yet doing the 3d representation inside itself, which makes it harder to define something like 'ears' and 'tail'