You say "not so", but you aren't actually contradicting what I said. Duplicating mathematical relationships, which I'm not even sure is an accurate description of a simulation, is still not the same as duplicating real objects.
It is an accurate description of a simulation. They all attempt to duplicate the relevant relationships as much as possible.
Sure, it isn't the same as duplicating real objects. Replacing a mechanical phone line routing system with an electrical one is also not duplicating the mechanical device. That doesn't mean it doesn't do the same job.
Even if that's the case, we'd have the difference between a perfect description/depiction of a thing and a thing itself.
And that's relevant how? We don't need an exact duplicate, only one that copies the essential behavior of the original.
No, I'm saying representing the mathematical relationships of something isn't the same as duplicating it. To interact like a human, the machine needs a body. We can't just simulate its legs. We can't just simulate its eyes. We can't just simulate its nerves and muscles. But we can just simulate its brain?
Does a quadriplegic not qualify as human? Are they sub-human if they are also blind? You overstate the need for a body a bit. We all agree they'd need some sort of input from an environment, and the ability to interact with that environment. But saying it needs to be "just like a human body" is silly. You'd seem to be dismissing people like Helen Keller.
Are muscles required to be conscious? I think not, and you'd need a pretty good argument to claim otherwise.
No one is proposing just duplicating the brain without some sort of input and output is the way to go. You can go two routes with input and output though. One, you can have a simulated environment. Two, you can provide an interface to the outside world (speakers, microphone, camera, etc). Either one would do.
I mean precisely what you are seeming to argue above. That saying you need legs, or eyes, or the like to be conscious is silly. You probably need some sort of environment to interact with at least for some part of your life, but demanding all 5 senses, muscles, a skeleton, and the rest is pretty ridiculous. Consciousness clearly resides in the brain, not the eyes, not the muscles, not the ears, not the arms, not the legs, not the heart.
I think the former. But no, the simulation will not perfectly replicate the physical interactions of the brain. We can distinguish between the two. Representing something is not the same as recreating it.
First, you don't need "perfect" you need "good enough." Brain damage, variances in brains, mental problems, and a host of other things is evidence enough consciousness is pretty resilient. Heck, as far as we are aware you can't get rid of it without literally rendering someone brain dead. So if you make a model that duplicates the interactions of the brain within .001%, then there's no reason to think it wouldn't be conscious (again, assuming you give it some inputs and outputs for information).
We can't model things just with math if model means "recreate".
It depends on what part of the system we want to recreate. If we want to recreate the part of the brain that takes in signals on nerves and outputs signals on nerves, and does so in particular fashion, we are perfectly capable of doing that in theory. We can even add eyes and the like to it. Sure, you won't have "gray matter", but are you really saying that color or how a brain feels to the hand is where consciousness lies? It isn't in how it sends signals that operate the tongue, mouth, jaws, and vocal cords producing words? It isn't in how it interprets written scribbles into sensible language? It isn't in how it takes in the touch of a loved one and feels soothed? This is ALL about taking in information and processing it, not about being sticky, or a particular color, or whatever.