Suppose someone cuts off the finger of a magus. How can the magus affect the finger with his magic? Can he still affect it with R:Per magic? Can he affect something that the finger is touching at R:Touch? I am asking because Mentem magic can turn the caster's mind into a bird, and it's still the caster's mind, so it can fly and affect things by touch.
I understand it's also an Arcane Connection to the magus.
I am aware of Timothy Ferguson's Divisible Men in Sub Rosa 13.
Both are different issues.
Discussing with your troupe, you can conclude from this:
A severed body part is no longer a part of the body, both physically and metaphysically. A person's mind moved by magic is not a counterexample to that.
I can imagine specific magic - like from a Breakthrough - detaching body parts while preserving the body's 'metaphysical' unity, though.
Hmm, not sure. The finger is clearly an arcane connection to the magus, for a while. But the magus does not have an arcane connection to the finger. Maybe you could argue for the blood in both? The bone fragments, if any?
If I understand Arcane Connections correctly, the finger was once part of the whole, and thus is an Arcane Connection to the magus. The magus does not have an Arcane Connection to the finger. A hair is a connection to the owner, but the owner does not have an Arcane Connection to that hair. Perhaps if you have part of he finger (a nail?)/hair, you could argue that it is a connection to that thing, but it could be argued that the connection is superseded by the connection to the person. A stone from Vesuvius is an Arcane Connection to the mountain, perhaps to teleport there, but the whole of Vesuvius, or individual stones aren't Arcane connections to that single initial stone.
"Mystically, the Arcane Connection is still a part of the target, thus making the spell possible."
"Something, the connection, is an Arcane Connection to something else, the target, if the connection was very closely associated with the target, often by being a part of it."
Talismans and Familiars are explicitly stated be Arcane Connections to the Magus and viceversa, but that does not seem to be the case in general, from the Core book.
Of course, this may have been already clarified, amplified and discussed elsewhere, and I would be happy to be pointed at this discussion, as the main book and the section on the Intangible Assassin in HP are spare in what is presumably an important detail in the rules.
I wonder if a part of a part is a part of a whole?
That is, if a magus loses a finger, then later loses the hand of that finger, clearly the finger is a connection to the hand, and the hand to the magus, but is the finger a connection to the magus? Is the hand a connection to both finger and magus?
Similarly, if a magus loses a hand that is then divided up, does this affect the connection, or do all the parts provide a connection to the magus? Or does dividing the hand somehow destroy the connection?
I tend to think that the magus is part of a whole, and all the parts have at least some connection up and down the chain, but I do not have any persuasive rule on the point.