I'm talking about the patterns painted on the machine (I believe I specified this in my post, if not, then my apologies). When I said "the pattern '2'" I literally meant that shape.
Oh, I see. You mean the labels above the columns.
If you look at the video you will see this pattern painted on the machine along with other patterns like "4" and "12" (I believe these are the correct patterns, but if they're different, then whatever.)
It would be "32". 12 would be represented by a marble in an 8 column and a 4 column. This is a binary arithmetic machine--computer geeks breathe this stuff.
If you imagine those patterns as some other set of patterns... say, imagine you'd covered each of the "2" patterns with a green square, each of the "4" patterns with a yellow square, each of the "12" patterns with a pink square... and you don't listen to the audio, then you'll be viewing the system simply as a physical system.
Once you do that, then -- and only then -- can you discuss what the machine is actually doing without a brain state involved (e.g. the knowledge that the pattern "2" is associated with pairs of things).
So when you say "brain state", do you really mean "the interpretation of conventional symbols in a pre-established language"?
(You keep complaining about my always including brain states in the discussion, and then you refuse to get them out of the picture. When you drop them, then I can, and I'm trying to.)
You're misunderstanding what I'm doing. My complaint isn't about removing brain states from the picture--it is about the way you chose to define "physical addition". I won't get into it in this reply.
Look at the marble machine again and forget that you have any clue what the paint is supposed to symbolize.
Then you'll see it for what it is as a physical system.
My analysis in the long post was based on playing with the machine instead of watching the video. But it was not based on interpreting those symbols at all.
And it will then become obvious to you that it is impossible for you to determine the function of the machine. (In other words, once you forget that you know what the pattern "2" is supposed to represent, suddenly those other conditions you associated with the value of a pair... they stop having that value.)
No, it's not obvious to me at all. In fact, quite the opposite. This is a simple puzzle--the physical machine would be a fairly decent puzzle, just handed to someone, without any rules. The style of analysis that I suggested in my long post has nothing to do with what is painted there. You can put green squares on there if you like, but I would like to one up you and suggest removing all of them. It's still possible to figure out what the machine does.
Except to say you can run marbles through channels, everything else is a guess, because lots of things are possible.
Only the descriptions that match what the machine actually does are possible. And a description of this machine's function is a description of its meaning.
Which means that the two-ness of the physical states of the machine which you described exists in your mind, and there alone.
Well, let me give arbitrary labels to these things just for discussion. Label the columns, from the right to the left, $, #, @, !, and *.
You can get a marble in column # by adding a single marble to column #. You can also get a marble in column # by adding two marbles to column $. So one marble input into column # is the same as two marbles in column $. All of this is simply how the machine behaves.
And that is where the two-ness of the number in column # is.
There is also a corresponding two-ness of the number in column @; that would be the fact that one marble shoved into column @ causes the machine to get into the same state as two marbles shoved into column #. And since column # has a two-ness equivalent to the marbles you can shove into column $ to get it, then column @ has a mega-twoness about it--a twoness of a twoness. That is, if you shove two marbles into column $, and you shove two more marbles into column $, you get the machine in the same state as shoving one marble in column @.
Note that nothing in this explanation appeals to the interpretation of pre-established symbols.
The machine behaves this way regardless of how you guess that it does. The only issue is figuring out how it works. But "how it works" is simply how that machine works--so it's all in the machine.
Your claim that it's impossible to figure out what this machine does is simply wrong.