This proves that you and another can be in a postition that gives you knowledge that you gathered simply by being cognisant and that this knowledge is not obtainable by outsiders despite their cognisance.
I see a few things wrong with the arguement:
1) Déformation professionnelle
– the tendency to look at things according to the conventions of one's own profession, forgetting any broader point of view.
-...because when I perform this thought experiment I only see what it proves; what I have previously stated. However I am forced to admit that it is possible that suffer from this fallacy as well.
– the tendency to see patterns where actually none exist.
-There is no relation to the thought experiment and the existence of a soul.
– perception that something is true if a subject's belief demands it to be true. Also assigns perceived connections between coincidences.
-There is a similarity between the thought experiment and the given explanahat and the soul but that does not make them alike even if you wish them to be alike because of your beliefs.
furthermore, what if you took identical people just like your thought experiment, but you had as many people as there are colors, each fitted in a different color. All you can descerne is that you are wearing what ever color you are wearing and you are in what ever room you are in and you are not the others or in the others' rooms. But you could have done this if you were all the same colors with the same rooms and STILL outside observers would be none the wiser.