> A cognitive system (assuming these models and the brain are both examples of this) needs to proceed from state A to state B as it processes information

Is that all it needs to do? A rock, in response to a sound signal (make it as informative as you want) can also be said to go from state A (molecules at rest) to state B (molecules vibrating in response to the sound). Is the rock a cognitive system?

Or let’s go up a level of complexity. Is a thermostat a cognitive system? It doesn’t just go from state A to B but measures changing stages against a reference. Is it a cognitive system?

> The time interval between these states can be arbitrary, it seems to me (setting aside problems with disconnecting the mind from its substrate, which does of course need rhythms at various frequencies; oxygen at a higher frequency than sugar, and so on)

Not sure how you land on this. Going from A to B, in your definition, is a purely internal state transition, right? If the motivation to go to state B is external (as will often be the case with a conscious agent), and the system is offline entirely while it switches from A to B, how is it to reverse or stall its transition if external signals contradict the earlier decision?

It’s a very bizarre definition of consciousness, that you don’t need to be in time. Seems to break the word beyond meaning, and allows it to be applied to any system capable of change.

> I'm not sure that going from A to B quickly, or slowly, or with intervals of a thousand years affects that entity's consciousness in of itself

It’s not about the speed of transition from A to B. Instead it’s about the internal processes being temporally commensurate, and entrainable to environmental periodicities.

All of biology (plants and many bacteria included) has its dynamics are organized around an internally generated rhythm. This rhythm entrains to the external environment, shifting its phase to match (mismatch leads to issues like jet lag: a place where your consciousness shows its temporal boundaries as it is abruptly subjected to an environment out of sync with its current phase tethered to another location). Crucially, the internal rhythm continues to run in isolated conditions (total darkness), and have been measured to be around 24 hours, but slightly off, within and across species (and the same holds for endogenous tidal rhythms, which also don’t exactly track tidal period left to themselves).

Everything, including learning and memory, but also sleep, sensory and locomotor function, shows organization around this internal temporal axis. The key advantage this gives, evolutionarily, is anticipation. The sunflower rises to face the east, not in reaction to sunrise, but in advance of it (many lovely YouTube videos of this), so it can maximally extract the nutrition it needs from whatever sunlight it can get. A purely reactive system would waste a ton of time after sunrise getting subsystems ready to respond.

Now, there is no broadly agreed theory of consciousness that points to these oscillations as the source. For one, Cyanobacteria and plants have them, a too much of science has rested on the baseless assumption of consciousness being some unique, or advanced thing.

But the evidence is rather overwhelming that consciousness is very much shaped by these internal oscillations. Deep cave experiments have shown what happens to cognition, and consciousness, when the clock free-runs (that is, keeps cycling with no entraining light or temperature signals from the environment). Studies have also shown that restoring the amplitude of these rhythms in patients with “diseases of consciousness” leads to improvement of symptoms.

There’s also a LOT of molecular evidence showing how the circadian clock affects learning and memory. Most critically, actual synapses are never static. Major components are on a 24 hour cycle, and recent research has shown that major clock proteins are at the synapse organizing its dynamics, and synaptic proteins critical to learning and memory loop back to affect the clocks phase and amplitude.

Timing is, beyond doubt, a huge aspect of what biology is. And every bit of evidence we have, from the molecular level to observable behavior we can feel ourselves, says that consciousness is fundamentally linked to how the body organizes its internal rhythms and responds to external time.