What I meant by this is the gravitational influence of N particles is the sum of the gravitational influences of each of the individual particles, and is therefore a strict function of their individual gravitational influences. If you give me any collection of particles, and tell me nothing except their gravitational fields, I can tell you the gravitational field of the system of particles. If you tell me the intelligence of each of your neurons (0), I cannot determine your intelligence.
A better mind than Tuxedage could almost certainly keep up the 'feel' of a flurry of arguments even with a schedule of breaks. I myself have had people feel irritated at me where even if I talk to them with days in between that I seem to do so. If I can do so accidentally I'm certain a superintelligence could do it reliably.
Also, I'm unsure of how much an AI could gather from a single human's text input. I know that I at least miss a lot of information that goes past me that I could in theory pick up.
An AI using timeless decision theory could easily compensate for having multiple AIs with unshared memory just by attempting to determine what the other AIs would say.
Step one involves figuring out the fundamental laws of physics. Step two is input a complete description of your hardware. Step three is to construct a proof. I'm not sure how to order these in terms of difficulty.