A solution to Mary's Room (Knowledge argument)

Mary's room is a philosophical thought experiment that goes as follows: Mary exists in a monochromatic room but she studies neurobiology and science until she knows absolutely everything about the physical/material process of colour perception in human beings and about the wavelengths emitted by everything she will ever come across. She then leaves the room and sees colour outside, does she gain anything from this action?

To most people it feels as though she does, but that is just intuition, which is notoriously unreliable. In order to answer the question we have to make some assumptions; specifically we need to make an assumption as to the nature of a human mind. If a human mind is some sort of magic entity separate from material reality then it is likely she does gain something from being able to see colour because she could not know how her own magic-mind-stuff will react to seeing colours purely from physical/material information. However, if a human mind is completely an emergent property of the physical/chemical/biological stuff that makes up a human brain then she does not gain anything from being able to see colour.

My argument:

If Mary knows absolutely everything about the physical process of colour perception in a human being then she can use this information to imagine a human being seeing colour. She can not only imagine this but her mental simulation of a human being seeing colour can be completely accurate and contain every detail of a human being seeing colour including all the activity of the human's brain. For argument's sake let's make her simulated human "sim-Mary" an exact duplicate of herself only outside seeing the colours she knows every detail about.

Now what can we say about sim-Mary? sim-Mary's brain must produce an identical copy of Mary's mind because we've assumed that minds are purely a product of the physical stuff that make up a brain and Mary knows everything about that physical stuff so can imagine an exact copy of all of that stuff thus an identical mind (otherwise there would be a contradiction). Thus sim-Mary and sim-Mary's mind must react precisely the same way as Mary & Mary's mind to seeing colours outside (otherwise Mary doesn't know something about how colours are perceived & hence a contradiction). Therefore Mary know exactly how she will react and experience colour even before she steps outside the monochromatic room.

Hence Mary gains absolutely nothing from leaving the room because she has effectively already done so completely within her own mind.

The flaw:

There is one major flaw in my argument, which reveals that the very question is flawed. If Mary can imagine every detail of her own mind & perception within her own mind then this creates an infinite recursion because sim-Mary could imagine a sim-sim-Mary imagining a sim-sim-sim-Mary imagining a sim-sim-sim-sim-Mary etc.... As a result Mary's mind and imagination must be infinite in it's memory and computational capacity. A human being's brain is not infinite in its capacity so it cannot learn all the information about itself. So unless the perception of colour requires only a tiny fraction of one's brain/mind the premise of Mary's Room is impossible; Mary simply cannot know everything about how colour perception occurs in human beings.