...me...
I'm not entirely sure what you mean. It appears that you're either making a point that I agree with (no being, no matter which way they perceive time, can be aware of events occurring in times of increased entropy, which we know as the future) or you're saying that beings cannot perceive time backwards. I'll concede that that's probably true, but again, that was a thought experiment and not a suggestion that they exist.
It's stranger than that. I've sort of hypothesised in a previous post that there
are consciousnesses working in the back-arrow direction. However, consciousnesses as we know it are working in the forward-arrow direction, because they're built upon forward-arrow processes, in which future is unknowable (although predictable given clues, of course) and the past is at least viewable (but of course becomes blurred in detail as they retreat into the past). I think quoting the next person on
might help me restate my rather esoteric point a bit better, though...
Stephen Hawking explains it best in A Brief History of Time. We perceive time as single-directional and constantly moving because of the way our brains work.
(my emphasis)
Our consciousnesses and the brains they sit on are so intrinsically linked that I don't consider this a useful argument. If consciousness arises from the way a brain reacts to past events and leads to future changes to the way the world is then consciousness is exactly that. Should there
be any possibility of reverse-arrow systems co-existing in our universe (i.e. "inevitability" reversed in some way then the very same substance of our brains could even 'house' reverse-arrow causality consciousnesses, independently 'thinking' of themselves via their reverse-arrow processes and being as unable to conceive of the counter-directional arrow-beings such as us as we are am of them. (Although I'd tend towards it being different anyway, our state of matter being as per their quantum fluctuations, and vice-versa, or rather something else not so obvious that we cannot perceive.)
No, that really doesn't sound like an explanation. (And because there can be no useful information-passing, I'm not suggesting that precognition is backward-beings whispering details to use that we will have whispered to them, earlier in their time. Darn, I could easily get misinterpreted here, though sounds like an idea for a short SF story at the very least...)
And...
As for looking backwards in a GoL to predict N-1, no, you cannot. First of all because the game can begin in any configuration. Thus there may never have actually been an N-1 line.
That point is well made, and certainly one that I hadn't caught. And I'd be rather hypocritical to (given my "there never was a beginning, it's just the pole of a sphere curving round" hypothesis, which might incidentally also be adapted to explain Expansion in the early universe) suggest that there
is a beginning, but I was sort of going with "if we can run a simulation forward from a
definite start, then the running backward could find that definite start.
The point you raise, though, shows me that my plan on finding "the" unique history is flawed. For every state at N, I was planning on rejecting all N-1 states that were not themselves viable (e.g. their precursors would need different overlapping pre-precursor pixels to create them.... wait.... superposition of states.... Quantum! Sorry, probably no relation and, but it's an idea to jam with at a later date.
), or going further and rejecting all N-1 states that purely led to a whole set of N-2,3,4,5... states that were not viable... But if there
is a starting state that you're deliberately retreating to (as a function of reversing an end-result that came from whatever you caused) then at some point there
must be a position down one of those 'trees' that is the same as the forward-facing initial state (from which you derived the 'true tree' and plucked the backwards-facing initial state). Apart from knowing and referencing Line# to ensure you're at 'Line zero' (which is a bit limiting, although as 'God' of the system, you have every right to do so) how would the system know that this is the intended precursor? Rule 110 does not produce cyclic combinations (if my analysis of it is accurate enough, given it shifts ), so there's no way you could actually find a negative-line that has an alternate precursor state. But for other rules, that's not necessarily the case.
[And at this point in composing this post I had to temporarily abandon to help out with a delivery, so my stream of thought has been interrupted and is probably disjointed. Just so you know.]
You're left with an interesting situation, in the general case of Rules, whereby for any given 'initial' state of a backwards-facing AntiRule system there are multiple possible 'ends' (i.e. origins) that by our classical view can cause the arbitrary endpoint in a forward direction. (This is easily demonstrable by running any number of classic GoL boards that result in a completely dead board, just one stable end-point that will never change or a metastable repeater. There's loads of ways to get each one of those results, so starting with such a result and attempting to work backwards can give rise to loads of intermediates. And that's completely ignoring the fact that stable (including empty) and metastable repeating patterns have the option of 'becoming' their immediate precursor pattern at any point in the backwards-going history, so even if you don't have an unlimited number of origins that eventually become those states (which you do) you have an unlimited range of ticks (of or above a given minimum) in which that process happens/becomes. Sorry, I know what I mean there.)
Anyway, so I take what you mean about there not being a unique history, and I think that topples the strictest interpretation of what I'm talking about, but I quite like how it leads to 'quantum state' intermediaries (perhaps a superposition of N-1 possibilities, leading to 'alternate futures', of the kind I normally say can't happen in a forward-facing world, and indeed this may be a paradigm shift in my thinking regarding the deterministic nature of the universe, if there's a useful philosophical analogue to be had here... i.e a fully and provably deterministic arrow of time in one direction
if being 'lived out' in the opposite direction produces... uncertainty... Deep.)
Now what. (Sorry, it's been perhaps a couple of hours since I started to respond, as already indicated, I'd forgotten what else I was going to say...) Well, I'll take my cue from the next bit of quotable instead and see if I can resurrect my thoughts on the matter.
Secondly, as mentioned, there are unpredictabilities since any given line could have an infinite possible number of previous setups. This of course assumes Rule 110 is being used, as there are more simplistic rules which can be traced back, some rather easily. For example, some rules result in merely copying one line to the next w/o change.
Hmm, yes, I think I've already led myself down to that conclusion just from your first point. I must have already put everything into it. However, note that the simplest rules (e.g.... let's see, the one probably identified as Rule204) have a fully deterministic forwards
and backwards travel, the uncertainty 'merely' being that of 'time back to origin' if reversing. (I don't like the idea of definite origins anyway, not arbitrary ones imposed by 'controllers' such as us, anyhow, and in this system there's no inherent boundary other than the external record of which Line/Generation# you're on.) Interesting to note that Rule 110 (and Rule 124, which has the opposite directional bias but can otherwise be considered identical) are apparently the simplest Turin-complete systems found, and that might be an important factor. Simpler rules that are not Turin-complete might also be unable to support the situation as discussed.
And there's also the interesting fact (related to its Turin-completedness? I must read up on that possibility...) that 110 is a rule that a provable degree of non-repeatability (it always spreads by one pixel from any non-empty state... although that also means that not every non-empty state retreats viably down to the single 'big bang' pixel as placed on Line0 by the 'creator'. (As a Creator, I needn't even start it off on one pixel. Otherwise what is the 110-type Turin machine actually calculating, except an arbitrary but deterministic infinite progression from that one-pixel start? I think the idea is that you can start it off with something arbitrary (and not necessarily viably reversible in itself) and produce an actual result. Like the number 42!
)
Rules that do have repeatability (say more complex ones that examine more than three states, and 00011 becomes 1 in the centre, while 00010 does not, or vice-versa, and something similar (or a 110-like 'straight' constrainer) on the other side of the pattern-matching can enter oscillating states. Much as classic GoL has the noted repeatability conditions. Such repeatability (including static systems, repeating on a 1-tick cycle) encounters the situation noted above.
But I'm afraid that I now think that
I am now going round in a circle, being unable to discover the enlightened conclusion that I was originally hoping to arrive at while considering this.
TL;DR; version: You make good points. I'm rethinking my philosophy on determinism. I still think there's something to be worked out.
I also spent a little time last night (more than the half hour, but not enough to complete the task) working on the Rule-following program that I discussed I might. I didn't get to finish all the tidying up of code that I meant to, even
before implementing the reversibility code in full, so I've scraped it back down to just the generic Rule-following script, removing the half-complete reversibility search. Most of what you'll see is really just nice-procedures for interpretting the inputs and nicely formatting whatever output it has. All done from scratch, because while I have some homegrown libraries, they're even more horrible to read than the ludicrously badly commented version you'll see below.
(I than added in the code, but it looks like I've hit the character limit. Actually, wasn't surprised at that. So another post follows with that info in.)
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