Since I have more time now, another reply.
First off--I didn't define a brain as a symbol system. In fact, I never even gave you a definition for brain. Therefore, one has to wonder where you got that this was my definition. If it wasn't from me, that leaves only you.
Now, you have no idea what symbol manipulation is, and no inclination to find out. You instead simply want to declare your expertise about it, and accuse those who do understand it of committing grave errors in thinking. When I finally figured out the exact nature of your error and pointed it out, instead of manning up and admitting you were wrong--you simply accused me of talking "shop talk" and trying to confuse you.
So I'll say it once more. A symbol is simply a uniquely identifiable state of a system that uses a series of transformations. These symbols are simply steady states of the system under the various transformations that the system performs. These symbols need not represent something--they just transform in particular ways given these transformations. What makes a particular instance of symbol that symbol per se is simply that it has the same effect on all transformations as any other instance of the symbol would have; what makes symbols different is that there exists some transformation that can distinguish them--that is, that for some transformation there is a different effect on one than there is for another.
Given a set of symbols and transformations such as the above, and an input, then you can perform analyses on the input using those symbols. In fact, we can define "input" into this system as some mechanism by which a particular set of symbols can be produced that reflects some state of the external world. For example, if you had a touchpad interface, and a grid of a particular symbol we call "1"; and pushing on it flips the symbol to another one that we call "0", then that is an input--and that can be analyzed by this system by transforming those two equivalence classes. Now per your account, I had to actually say that "1" meant "not touched" and "0" meant "touched", but really, nothing changes if I use 0 for untouched and 1 for touched. Or X for untouched and Y for touched. Or if I just left off all of the convenience labels, and simply said that there's a distinct symbol invoked when you touch the pad at certain locations with a particular pressure from when you don't.
But in all of those cases, there is a symbol in the system that corresponds to your touching the pad versus not touching it. And whatever you call those symbols, the transformations of them can analyze that touching. And by "analyze", I simply mean that the symbols--as defined above--can be affected in various complex ways by what's being touched.
So if your touchpad can identify when someone draws the symbol "2" on it, then that means exactly what it says. It means that it can produce distinct behaviors in terms of its internally identifiable states (i.e., symbols) when someone draws the symbol "2" versus when someone doesn't. Given a device does this, it does not matter what things are "supposed to represent"; that state will be there sometimes, and it won't be there other times, and the times it will be there would be when you draw that symbol, and the times it won't will be when you don't.
It's symbol manipulation. It's not poetry.