Hal Finney writes > Can we imagine a universe like ours, which follows exactly the > same natural laws, but where time doesn't really exist (in some > sense), where there is no actual causality?
You yourself have already provided the key example in imagining a two dimensional CA where the second dimension can be taken as y instead of t. > If we can find a reasonable interpretation... of a pattern in > the [this CA] universe as something that we would consider a > conscious observer in our own universe, then we would be right > to say that this CA universe has consciousness. I would be VERY HAPPY to abandon my belief that somehow time is special. It's very annoying to suspect myself of simply having a failure of imagination, in that I could not---as Einstein perhaps did---see our 4-D block universe as just any old 4-D continuum. But I encounter a runaway reductio that smashes up my attempt to *believe*. Okay, so suppose we have a book one trillion times as large as Wolfram's (or as big as we need to have), and we cut out all the pages and line them up so that we have a two dimensional layout that is recognizably a conscious entity. This now, as you know, no longer exhibits any *time* at all; it is a "succession of frozen states", that is, each horizontal line of the CA is, as you describe, connected to the next only by..., only by what? Well, it seems that it is *we* who spot the connection. We guess and then accept that there is a rule that associates each horizontal line with the next one. Not so simple as the rule you give (i.e., s[x,t+1] = s[x,t] XOR (s[x-1,t] OR s[x+1],t]), of course, but nonetheless entirely objective after we see it. We can call it time---or not---, just as you also point out. (I will later claim that what is missing is the underlying continuous machinery, but to do so right now would be to miss the point of your argument.) So we have this sequence of horizontal lines which are connected by a rule. The input to the rule is line N and the output is line N+1. Indeed, I am tortured by the resemblance to quantum states: we seem in our own comfy universe to have a succession of states connected only by the Schrödinger equation. One interesting point about this two dimensional consciousness is that it's not clear (to me) whether it needs to persist in our time. That is, would it make any difference if we destroy this large two dimensional map? On the one hand, since it seems to be independent of time, the answer would be "no", but on the other, what if Hal Finney and Wei and whoever, is right about UDs and measure, and destruction of the 2-D layout makes it "harder to find" when all the OMs are being counted up by Heaven? I don't know. But anyway, for me, the horrid reductio always kicks in at this point: what should it matter if these 1-D lines composing the layout are scattered in space? What does it matter if they're chopped up? Is it really only the case that "they're harder to find"? That they're "less manifest" in Everything? It's too hard to believe. Do we not need a *continuous* parameter? Are we not back with Zeno wondering how the arrow can move if it's just in a succession of instants? It seems to me that Zeno would have been right for any *finite* number of locations (or instants), and there would have been no such thing as true motion. Lee