Could infinitely many physical operations finish in finite time?
Thomson's lamp is switched on, off, on and off at ever shorter intervals. The total time can converge while the proposed final switch state has no limit. A finite duration therefore does not guarantee that an infinite program has a well-defined output. OPH's finite executions specify actual events and records, and its continuum limits need convergence bounds for the quantities being claimed. A limit of descriptions is not permission to execute infinitely many elementary operations or extract an undecidable answer. This separates Zeno's finite travel time from a physical computer doing endless work. Any proposed machine that completes such a task would need a physical realization beyond the finite observer model.
See also How does OPH answer Zeno’s paradox?, Would a theory of everything let us predict every event?
Also in Chapter 16: Why Does Time Run, and Only One Way?, Chapter 37: Why Does the Loop Have No Beginning?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 13: What Is One Piece of Reality Actually Made Of?watch a universe make its own particles