Spacetime (might be) infinitely large, but that doesn't imply that there is infinite matter or energy.
That said, this is kind of a dumb argument because far lower k values have lower BB(k) values already exceed the apparent information value of the universe at any given instant. Maybe there is infinite energy and matter, but that's also irrelevant if we can't perceive more than a finite subset of it.
Edit: well, i guess what would matter would be the information value of time, multiplied by enough bits to store the machine—I'm not sure i'm literate enough in the area to compute that. But, assuming that the heat death of the universe reaches a single (possibly compressed) end-state, it should still be finite—it's seeming quantized, anyway.
That said, this is kind of a dumb argument because far lower k values have lower BB(k) values already exceed the apparent information value of the universe at any given instant. Maybe there is infinite energy and matter, but that's also irrelevant if we can't perceive more than a finite subset of it.
Edit: well, i guess what would matter would be the information value of time, multiplied by enough bits to store the machine—I'm not sure i'm literate enough in the area to compute that. But, assuming that the heat death of the universe reaches a single (possibly compressed) end-state, it should still be finite—it's seeming quantized, anyway.