Thanks for the comment!

Yes, it's literally a physical difference, but, by hypothesis, it had no influence on anything else in the brain at the time, and your behaviour and reports would be the same. Empty space (or a disconnected or differently connected neuron) could play the same non-firing neuron role in the actual sequence of events. Of course, empty space couldn't also play the firing neuron role in counterfactuals (and a differently connected neuron wouldn't play identical roles across counterfactuals), but why would what didn't happen matter?

Do you expect that those temporarily inactive neurons disappearing temporarily (or slightly more realistically, being temporarily and artificially suppressed from firing) would make a difference to your experiences?

(Firing rates would still be captured with sequences of neurons firing, since the same neuron can fire multiple times in a sequence. If it turns out basically every neuron has a nonzero firing rate during every interval of time long enough to generate an experience, if that even makes sense, then tortured walls could be much rarer. OTOH, we could just make all the neurons only be present exactly when they need to be to preserve the pattern of firing, so they might disappear between firing.)

On finding similar patterns elsewhere, it's because of the huge number of particles and interactions between them going on and relatively small number of interactions in a morally relevant pattern of activity. A human brain has fewer than 100 billion neurons, and the maximum neuron firing rate in many morally relevant experiences is probably less than 1000. So we're only talking at most trillions of events and their connections in a second, which is long enough for a morally relevant experience. But there are many ordered subsets of merely trillions of interacting particles we can find, effectively signaling each other with forces and small changes to their positions. There are orders of magnitude more particles in your head and similar volumes of organic matter, like wood, or in water, which might be more "active", being totally liquid. There are at least 10^25 atoms in a liter of water, but at most 10^14 neuron firing events in a second in a human brain.

Hmm, but maybe because the particles are also influenced by other things outside of the selected neuron substitutes and plausibly by each other in the wrong ways, appropriate subsets and mappings are hard to find. Direct influence between more distant particles is more likely to be messed up by local events. And maybe we should count the number of (fairly) sparse directed acyclic graphs with n vertices (for neurons or particles), but at most thousands of connections per vertex on average (the average for humans).

One simplifying assumption I'd probably make first is that any neuron used at least twice in a sequence could be split into multiple neurons each used exactly once, so we can represent the actual events with a topologically sorted directed acyclic graphs, plotted with time on the x-axis. If you were to draw each neuron when it fires and the signal paths with time as the x-axis (ignoring actual spatial distances and orientations), you'd see the same neuron at different points, and then you'd just treat those as if they were entirely different neurons. Even with counterfactual robustness, you can unfold a recurrent neural network and in principle preserve all functionality (but in practice, timing would probably be hard to maintain, and functionality would likely be lost if the timings are off). This simplifying assumption rules out IIT and Recurrent Processing Theory as too strict in one way.

We could also reduce the number from trillions by using much smaller conscious animal brains. With some mammals (small rodents or bats), it could be in the billions, and with bees, in the billions or millions, and with fruit flies, in the millions, if these animals are conscious. See this wiki page for neuron count estimates across species. Their firing rates might be higher (although apparently invertebrates use continuous rather than binary neuron potentials, and mouse neuron firing rates still seem to be below 1000 per second), but then it's also plausible (although not obvious) that their shortest morally relevant time intervals are roughly inversely proportional to these firing rates, so smaller.

The bomb trap example is very interesting! Can't be counterfactually robust if you're dead. Instead of bombs, we could also just use sudden overwhelming sensory inputs in the modality they're fastest in to interrupt other processing.  However, one objection could be that there exist some counterfactuals (for the same unmodified brain) where the person does what they're supposed to. Objects we normally think of as unconscious don't even have this weaker kind of counterfactual robustness: they need to be altered into different systems to do what they're supposed to to be conscious.

But pointing out that path takes a lot of information which might only be present inside the pointer, so I think it's possible that we're effectively "sneaking in" the person via our pointer.

Interesting. Do you think if someone kept the mapping between the states and "firing" and "non-firing" neurons, and translated the events as they were happening (on paper, automatically on a computer, in their own heads), this would generate (further) consciousness?

I often also use Conway's Game of Life when I think about this issue. In the Game of Life, bits are often encoded as the presence or absence of a glider. This means that causality has to be able to travel the void of dead cells, so that the absence of a glider can be causal. This gives a pretty good argument that every cell has some causal effect on its neighbours, even dead ones.

But if we allow that, we can suddenly draw effectively arbitrary causal arrows inside a completely dead board! So I don't think that can be right, either.

Doesn't counting the causal effects of dead cells on dead cells, especially on a totally dead board, bring us back counterfactual robustness, though?

To expand a bit on the OP, the way I've tentatively been thinking about causality as the basis for consciousness is more like active physical signalling than like full counterfactuals, to avoid counterfactual robustness (and counting static objects as conscious, but there are probably plenty of ways to avoid that). On this view, dead cells don't send signals to other cells, and there's no signalling in a dead board or a dead brain, so there's no consciousness in them (at the cell-level) either. What I care about for a neuron (and I'm not sure how well this translates to Conway's Game of Life) is whether it actually just received a signal, whether it actually just "fired", and whether removing/killing it would have prevented it from sending a signal to another that it did actually send. In this way, its presence had to actually make a non-trivial difference compared just to the counterfactual where it's manipulated to be gone/dead.

Another related point is that while shadows (voids) and light spots can "move" faster than light, no actual particles are moving faster than light, and information can still only travel at most at the speed of light. 

On your approach and examples, it does certainly seem like information is correlated with the stuff that matters in some way. It would be interesting to see this explored further. Have you found any similar theories in the literature?