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Arrows between events in causal graphs that skip over other events

Joseph Musser
Posted 6 years ago

Does anyone know the reason why the causal graphs show some but not all arrows between updating events that skip over a step? What do the arrows signify?

I put numbers 1-5 on the arrows in this graph from https://www.wolframphysics.org/technical-introduction/the-updating-process-in-our-models/causal-graphs-for-causal-invariant-rules/#p-319 that skip steps. Why these arrows and not other arrows that could have been drawn that would also skip steps?

graph
POSTED BY: Joseph Musser
9 Replies
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Joseph Musser
Joseph Musser
Posted 6 years ago

That is a helpful explanation, and it answers my original question perfectly. Thanks so much for taking the time!
POSTED BY: Joseph Musser
POSTED BY: Ruggero Valli
Mike Besso
Mike Besso
Posted 6 years ago
POSTED BY: Mike Besso
Joseph Musser
Joseph Musser
Posted 6 years ago

I think I'm the one missing something, but I'm still just trying to understand this. Why aren't there orange arrows here where I've added red lines? (There are more I could draw.)

enter image description here
POSTED BY: Joseph Musser
Mike Besso
Mike Besso
Posted 6 years ago

For this number of iterations, I do not see any missing orange arrows. Am I missing something?
POSTED BY: Mike Besso
Joseph Musser
Joseph Musser
Posted 6 years ago

Yes, so why aren't there more of these orange arrows? What makes the five that are there more significant than other arrows you could draw that point to future events caused by each event?
POSTED BY: Joseph Musser
Mike Besso
Mike Besso
Posted 6 years ago

I think that the orange arrows point to all future events that are caused by this event, not just the immediate next event.
POSTED BY: Mike Besso
Joseph Musser
Joseph Musser
Posted 6 years ago

Thanks! I should have clarified that I'm only asking about the orange arrows. There are orange arrows from each updating event to each immediately-following updating event, as you'd expect, but there are also five orange arrows that connect to events that don't immediately follow, jumping ahead if you will. More such arrows seem to be possible, so why only those five, and why those five at all?
POSTED BY: Joseph Musser
Mike Besso
Mike Besso
Posted 6 years ago

I'm just getting started with Wolfram Physics and really wish I had more time to experiment. Taking a look at your example though, I think (and am by no means certain) that the diagram is showing two separate graphs.

The gray arrows take us from one state to the next state after the application of the rules.

The orange arrows show us what events lead to all future events, not just the next event.

I'd love to hear other interpretations.
POSTED BY: Mike Besso
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