Okay, so I agree that this machine can be used for multiple purposes. A farmer might use it to keep track of eggs in the henhouse. The builder might have intended it to balance his checkbook. And I have already stated that this sort of thing is not a kind of thing you can guess at. So if this is what you mean, I agree.
You know those folks I mentioned who have one-side-blindness... the ones who see only half the world but can't tell that they're missing the other half... who'll trip over a footstool and swear that it wasn't because they couldn't see it?
Your way of thinking on this issue is precisely like that.
You find it impossible, not just to
accept a view of the marble machine as an object, but even to
contemplate such a view.
How do you know that the particular relationships in the machine's construction which you're focusing on are significant to its use, rather than coincidental? And how do you know that other relationships of the machine (say, its height, width, and depth, or the length of the channels) aren't used as indicators to perform further mathematical functions?
Perhaps if the marbles come through a rectangular machine, you're supposed to multiply the result by 10, and if they come through a square machine, you're supposed to multiply by 7.
Or perhaps the purpose of the machine is only to route marbles along those channels and through those baffles, and the particular mathematical relationships are coincidental, or are there because this part needs to fit into another part which has those relationships for reasons which are significant to it instead, or because the designer was a mathematician and an artist who found the relationships elegant.
Perhaps this machine works with another machine that uses the positions of the marbles to do something other than adding numbers. Perhaps it's the color of the marble that matters to the other machine, and the physical set-up of the marble sluice is to route different marbles to different positions to have their colors detected by the proper device.
Perhaps this device's only purpose is to limit the number of marbles moving through a certain point at a certain time to fewer than 7 at a time.
You have no way of knowing.
Of course, if you're exploring all the possibilities, and you find one like "it could be used as an adding machine", and you decide that there's very little chance that a human being would set it up like that accidentally, and you decide that there's very little else a person might want it to do, then you might think "It's got to be an adding machine."
But notice all the information you had to drag in from elsewhere. And notice that this information has to do with how human brains tend to act.
But the machine itself, if it were self-aware and if it knew everything that could be known about its body and nothing else -- in other words, if we're looking at the circle with just the machine in it, the machine as an isolated system -- the apparatus itself has no way to guess all these things, and so every possible use of the machine is just a good a guess about its body's purpose and function as any other.
(Odds are, though, that the machine won't come up with any ideas about its body which begin with "Suppose there were some other being using my bodily functions symbolically....")
So your world, in which our only choices are folks using the machine to add stuff, is a partial world, and you're not only ignoring the rest of the world, you're refusing even to see it.
Yet again -- and for precisely the reasons I've explained -- you find yourself right back smack-dab in the circle of the information system, which includes the machine and information in (which is to say, a physical state of) at least one human brain.
All I'm asking you to do is to take your eyes off that system and look at the other circle for a moment, the one with just the machine in it.
But you refuse to look there, even momentarily.
As long as you listen to what I'm saying about the system that includes just the machine, but you keep your eyes glued to the "information system" circle that also has a human brain in it, and you try to interpret what I'm saying about the machine alone into that picture, what I'm saying isn't going to add up.
That's why what I'm saying seems confusing or wrong to you.