| dc.description.abstract | In this three-part thesis, Part I is an examination of the measurement process in classical Hamiltonian mechanics. This part is concerned with the tradeoff that exists, when measuring any observable of a system, between the disturbance inflicted upon the system and the information that can be extracted. The main result takes the form of a Heisenberg-like precision-disturbance relation: measuring an observable leaves all compatible observables undisturbed but inevitably disturbs all incompatible observables. The magnitude of the disturbance (the analogue of Ò) is found to be proportional, in a sense that is made precise, to one’s initial uncertainty in the ready-state of the apparatus—a quantity that relates to the temperature of the apparatus.
Part II of this thesis develops a model of the computations taking place in the deliberative decision-making system of rodents, during wakefulness and sleep, with focus on the role of hippocampus (HPC). In this model, medial prefrontal cortex performs high-level planning, and then tasks HPC with fleshing out the details of the plan, as needed. We describe this planning task of HPC as an optimal control problem, which allows us to draw insights from the powerful mathematics of optimal control theory. The model makes novel testable predictions, provides insights into memory consolidation during sleep, and offers a paradigm capable of accommodating a wide range of observed phenomena, such as the theta rhythm, the slow oscillation, spindle oscillations, sharp wave-ripples, θ-sequences, for-ward and reverse SWR-sequences, the formation and strengthening of episodic memories, and a need for two modes of operation—online and offline.
The two parts described above are the main content of this thesis. Part I falls within the purview of classical theoretical physics, while Part II falls in that of computational neuroscience. The two may seem unrelated; however, while each part is self-contained, I see the two as connected. Part III of this thesis is my attempt to provide an outline of a bigger picture, which sees the foregoing as lines of inquiry towards the same far-reaching conjecture—one which has had a strong pull on my imagination during my PhD, and which I hope to be able to address in the future. This conjecture is that the probability calculus of quantum mechanics holds a kind of normative status for a class of decision problems involving intertemporal choice under uncertainty—a class of problems of great importance to artificial intelligence, brain sciences, economics, and, I argue, to physics too. | |
