Ok, I'll put it back into context for you and we'll move on from there.
Remember, the topic is symbolic information systems, such as adding machines and simulator machines.
Yes.
Okay. There's a general thing you keep bringing up over and over. So let's just start right here.
But what about our marble machine? What sort of aggregation can it peform, and under what circumstances?
...
Without a brain state to determine the "meanings" of the patterns of paint on the machine, they might as well not be there. You need a brain to assign those meanings and to interpret them.
Without that, all you're left with is an object you can drop marbles through.
Your phrasing is still clumsy as hell, but I'm just going to wing it. By focusing on simulations rather than mere correlations between systems, what we wind up doing is examining things like this that have an
intended purpose. Like, not just the symbols, but the entire machine--the thing that the person who built it had in mind when he put the thing together. But part of this intent is the symbols--the guy who made this marble machine created symbols using the rocker.
So, the first thing you need to do is stop saying "brain state", because that's not what you mean. You're really after just meaning itself. So let me explain to you how this works.
You can prove this to yourself by viewing the video with the sound off, and ignoring the patterns of paint -- remember, inside our circle there's nothing that has any means of deriving any meaning from them. (Even if the machine were completely self-aware, this would still be the case.)
The problem, I surmise, is that you're imagining that the task of coming up with the meaning of the machine is one akin to mind-reading the builder, to figure out what he had in mind when building the machine. I'm going to suggest to you that this is simply the wrong approach. After all, even if you did somehow guess at what the programmer had in mind, all you're doing is deferring to his intent.
What you need to do, instead, is to study the machine. In particular, you need to pay attention to two things--entities, and transformations. In particular, when I refer to "entities", I mean "anything with an identity"; that is, something you can recognize. Something that is distinct from other things, and the same as itself. A transformation is something that takes entities and makes entities. This is a vague definition on purpose--these things can be anything at all. They're just that abstract.
But in the marble machine scenario, it's not that difficult. To figure out what entities are, you just observe invariants; that is, things which tend to remain the same. The marbles would do--and I take it we can start with our ability to recognize marbles, columns, relative position, and so on--unless you want me to explain how to identify those.
So, the marbles are entities. And the rockers are entities. Now we look and see what happens to the entities. We just jump in and play, and look for things. Put a bunch of marbles in. Put a few in. It's not too long before we notice an interesting property--marbles either stay in a column, or they move left. Further study reveals another interesting pattern--if we start from scratch, and I put two marbles into the same column, I get one marble in a column to the left. It doesn't seem to matter which column we start on, this pattern holds. There's another invariant. It probably won't take that much more tinkering before we discover that if I put one marble into a column, and put two marbles in the column to the right, then I wind up with a single marble at the left. This seems interesting, because without that marble in the column, the two marbles would have put a marble there--so the system seems to behave the same if I put one marble into a column, or two marbles into the column to the right. So there seems to be a bit of a global pattern--and we can try to figure out to what extent this rule applies.
After some study, we might figure out that we can make any arbitrary number of rockers go to any position--just from a blank spot, put numbers in the columns we want rockers to the right in. And with our rules above, we note that we can also get a particular rocker into position by adding two marbles to the column in the right. Or four marbles to the column to the right. Then we may note that we can fill the machine to get the position simply by adding marbles to the rightmost column--and our desired arbitrary position will get set one column at a time from the left to the right. Then we may get interested in just adding marbles to the right to see how many states we can produce--and we note that when everything is filled, and we add one more marble, everything empties.
So by now, we note that every arbitrary position can be reached solely by adding marbles into the righthand column. Not much after that, we may learn that filling in the arbitrary positions manually--by dropping the marbles into the columns we want--and adding more marbles to the machine arbitrarily, produces the same result as adding enough marbles to make one position, then adding enough marbles to make the other one.
And thus, we learned about positional numbering systems, and the meaning of addition using them.
The meaning of the symbols derives from the relationships between the states of the system and the environment of the system. The entire exercise above is simply one of studying what the states of the system implies about the environment--the full theory of the machine, which can be discovered simply by studying what the state implies about the inputs--conveys the meaning of the machine.
Without a brain state to determine the "meanings" of the patterns of paint on the machine, they might as well not be there. You need a brain to assign those meanings and to interpret them.
The marbles react to their inputs in specific ways. Figuring out the meaning of this machine is simply a matter of studying what the states of the machine implies about the inputs. As soon as you build a full theory of this, you have discovered the meaning of the machine.
It's all there, in the machine.
Without that, all you're left with is an object you can drop marbles through.
Not quite. You have the machine reacting in specific ways to the marbles. And you have the states of the machine exposed--which, in this case, is the intended outputs. From this you have very real behaviors that you can study to figure out what the state implies about the environment.
How did you suppose
we discover meanings?
The only addition it can do is to channel the marbles at the top into a single group at the bottom.
Not true. See above. You just have to develop a full theory of the machine, and out plops everything from a positional numbering system to addition.
So let's use our other circle to describe the minimum system needed for this thing to work as an info processor.
Well, we need at least one brain capable of assigning values to different aspects of the machine, determining the rules of operation, and interpreting the results of the machine's behavior. (A programmer and a user or reader.)
Again, why a brain? All you need is something capable of generating a full theory of the machine. You're begging the question.
It might be one brain or more involved, but at least one is required.
Yes, obviously. The guy that built the thing. But that's just because it's a machine someone built.
The "world of the simulation" -- which is to say, whatever a simulation program is supposed to represent -- cannot be located in the simulator.
Maybe in general. If this marble machine was supposed to balance the builder's checkbook, it'd be impossible to figure that out without asking the designer. After all, the only thing it interacts with are marbles. But you're misunderstanding something very fundamental about how meaning comes to be. Everything you need to understand that the machine performs addition is there in that marble machine. It just requires studying the invariants.
It's a real machine, and it performs real transforms according to real inputs. And it obeys the laws of physics to do it. It's possible by studying it to figure out that it adds...
For the same reason you can't go and program yourself a new truck or a bigger house or clean laundry.
...but it doesn't haul freight.