Earlier quoted context omitted.
I actually came in here to ask for clarification on this. This sounds presumptuous. Couldn't there be thousands of neural networks which all receive an input signal, and we know how to interpret the output of all of these, as a signal. Maybe the neural networks themselves are all only 10 layers deep, but if they're all running in parallel - this defeats this point, right? I don't really know anything about it, though…
Combining a thousand networks into one signal is effectively one extra layer (though I don't think human neurons can actually handle a thousand incoming connections). The observation was a comment on how deep a network needs to be to perform useful tasks.
Purkinje cells can have on the order of hundreds of thousands of inputs.