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ADDB/TUM, Time Travel, and Fate v. Free Will


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#41 Christopher

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Posted 30 January 2003 - 01:44 PM

Una Salus Lillius, on Jan. 30 2003,10:52, said:

Possibility Number One:  There is but ONE time "line", that is there is but one chronology of events.  However the word "line" is a misnomer because although there is but one, in fact it tends to be more of a curly q thing such that once in a while you will see things happening out of sequence and even once in a while see a brief convergence because um, the "line" isn't a still thing but tends to ebb and flow.  Under this scenarior, the chronology would actually be that Rhade kills Dylan, goes forward with his mission, fails, encounters nu Trance (temporary convergence of present with future due to ebbs and flows), realizes he has to set things right, goes back, kills his younger self, and lets Dylan kill him, allowing Dylan to proceed with his mission.

Chronologically on the show that is not how it happened because of the fact that the time line is not straight but curly and hence the weirdness in chronology.
What you're describing is actually Rhade's worldline, his individual, subjective journey through time.  But the "graph" I'm describing plots that worldline on top of a chart of the universe's overall timeline, which follows a Y shape.  Rhade's worldline follows one branch of that Y, then loops back to the branching point and continues for a few minutes along the other branch before ending on the command deck.  (Or we could argue that the worldline of his body continues indefinitely in the other branch, since the body remained there even though it wasn't alive anymore.)

The thing is... if you follow Rhade's worldline from start to finish, then yes, it does take the form of a single line following a curlicue pattern.  But my point is, if an objective observer of events takes a look at one specific moment in history, say a given day of the year CY 10087, then that observer will see two different sets of events happening simultaneously, one with Rhade in command and another with Dylan in command.  Because Rhade's worldline loops back on itself, then an instantaneous cross-section of time within the span of that loop will contain at least two separate versions of that moment.  In other words, parallel realities.

It is still one universe -- it's just a quantum universe, able to exist in a superposed state.  Just like how an electron can pass through two different slits of an experimental apparatus at the same time, instead of just one or the other as classical physics would demand.  This really happens, in our universe -- what we're describing here is just a larger-scale application of the same principle.

Personally, I'm skeptical of this, for reasons I spelled out once in an article on the Andromeda Universe forum (well, twice, actually, since I reposted it in a later thread).  A superposition can easily happen with one particle, and routinely does, but getting a whole ensemble of particles into the same superposition of states at the same time is about as probable as building a 50-km-high house of cards in the middle of a hurricane and earthquake, and doing it with every particle in the universe is therefore too improbable to contemplate.  Or so my reasoning went.  But Stephen Hawking seems to believe the universe as a whole has a single wavefunction, and can thus be treated as a single "particle," and therefore possibly can exist in multiple superposed states.  I'm skeptical about that in real life, but I'm willing to accept it for the purposes of GRA, especially since it's already been established onscreen in BotL that "the wavefunction of the universe" is a real phenomenon.

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#42 Cardie

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Posted 30 January 2003 - 02:03 PM

I would have preferred the single timeline ADDB theory meself, and I'm fairly sure the rest of the writing staff would have, too. Now we could say that RHW could have brought about the changes mandated to DROM from above without bringing in the events of Ouroboros and setting up an alternate timeline. Considering that from that point we actually have two different shows, I'm not sure it wasn't an apt metaphor, even if it changes one of the founding principles. I do think that if an alternate timeline had to be established, the way it happened in O and TUM were the least insulting to the laws of physics, as Christopher has explained far better than I could.

And although these are alternate timelines, they occur in the same universe and it isn't at all surprising to me that Rhade would choose to sacrifice himself to be the one who by one act of will made that universe a better place than if he had continued the way he was going, a way that may be the path to apocalypse. Suppose a person graduates from college and is offered two different jobs in two different cities. One is that person's home town, the other is far away. The person chooses the one far away. The job turns out to be boring and dead end. The person marries a co-worker but that marriage fails. The friends made in the new city are not as treasured as the old friends. The person still gets to see family and old friends on visits to the home town, but their interactions are different because of the long distances that separate them. However, the old friends and family still exist. The home town exists. And then one day a strange being comes and tells this person that if he or she had taken the job in the home town, it would have resulted in acting one year later tp keep alive a child who will grow up to prevent the worst terrorist attack ever on America, one that would have left the country in ruins and chaos. The rub is that the person would have died while saving this child. And then the strange being says, "I have the means to let you go back and make the other decision while the world you're currently living in goes on without you apocalypse and all." Some people would say yes and some no, but it's not like the person would be choosing to save or to sacrifice completely different people. The difference in the parallel timeline would be the person's relationships to those others.

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#43 Anarch

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Posted 30 January 2003 - 06:12 PM

Christopher, on Jan. 30 2003,09:31, said:

No, I take that back, it's not so much physics as simple logic.  I say this over and over again:  An event that has happened cannot "un-happen."  Period.  You can't erase a moment of time, because erasure is change.  Change requires a "before" and an "after" -- the version of the thing that existed before the change and the version that exists after the change.  A single moment in time cannot exist before itself!  So the concept of "erasing the past" or "changing the past" is simply meaningless.  By definition, if there are two versions of a single moment, they both exist at the same time.  Neither one "replaces" the other; they exist side-by-side in parallel timelines.



It's also mathematically impossible (which is kind of the same thing).  To put it in physics terms, an equation must have a unique solution.  It can't add up to two different values at once.  So there are only two options, the two which Rommie and Sara spelled out in ADDB & BotL: either an event only happens one way, or it happens a different way in each of two separate timelines which subsequently do not affect each other's development.
Got to thinking about this the other day -- strangely enough, it relates to my research in an extremely oblique way --  and it occurred to me that there's actually a fairly standard mathematical dodge which invalidates your claim that "To put it in physics terms, an equation must have a unique solution.  It can't add up to two different values at once" while simultaneously linking every "possible" universe into one:

Riemann surfaces.  Or covering spaces.

[Busting out the math here, sorry.]  Look at the Riemann surface of the complex logarithm function.  Each point in the complex plane gives rise to infinitely many preimages (technically, the inverse map has an infinite fiber), all of which locally look like the plane itself.  Weirdness only happens when you go "around the circle", so to speak -- when you take a non-trivial path around the branch point z=0 -- and even though the path in the plane is just a closed loop (you returned back to where you started), the lifted path is actually an open-ended line between two different points whose sole connection is that they both project down onto the same point.

[The standard image here is actually one-dimensional.  Take a loop, and suspend above the loop a bi-infinite helix -- think of it as a corkscrew that's infinite in both directions.  Go around the loop once {i.e. make a closed circle downstairs}; when you lift that loop up to the corkscrew, it actually moves you up or down a level {i.e. doesn't return you to where you started.}]

Why mention this?  Dunno... except that it's possibly that all these supposedly-distinct "parallel universes" are actually just parts of "the One True Universe" where you've gone around a branch point in space-time.  Destroy one "parallel" universe and major weirdness ensues.  Typically one can't pass around a branch point except under extreme circumstances (e.g. tesseracting Alice-strings, he tech-fu'ed) and therefore one's "visible" universe is essentially just the projected loop downstairs... but just because we can't pass over that branch point (well, really, the discontinuity which induces the branch point) doesn't mean the things aren't connected at some higher level.

This could also explain the ADDB/TUM dichotomy:  in ADDB, Dylan went "back in time" but stayed on his own "loop" -- technically, remained on the canonical lifting of the base space relative his original base-point in the covering space -- while in TUM Rhade actually shifted between liftings, thereby moving into a "parallel" universe.

Or, given that I haven't actually seen the episode in question, maybe I'm just full of crap :)

- Anarch


#44 Christopher

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Posted 31 January 2003 - 09:07 AM

Anarch, I'm glad you're here to enrich the forum with math jargon that even I don't understand.  I've missed that. :D  :crazy:

Anyway, what you say about "looping around a branch point" reminds me of what little I've managed to dig up online about Alice strings.  Maybe it's the same thing.  So maybe what you're describing actually is the rationale RHW used in "Ouroboros" to justify the parallel timelines.  (Robert, are you still with us to comment on this?)

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#45 Bad Wolf

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Posted 31 January 2003 - 10:22 AM

I still say that parallel time lines/realities/universes *whatever you want to call it* is far more inconsistent with the Dromverse than a single time line *even* if it means you can change the past.
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#46 Anarch

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Posted 31 January 2003 - 03:59 PM

Quote

Originally posted by Christopher:
Anyway, what you say about "looping around a branch point" reminds me of what little I've managed to dig up online about Alice strings.  Maybe it's the same thing.

Could well be.  In this context, I guess you'd represent Alice strings by strings which "wrap around a branch point."  They look like they meet up at the other end -- and in some ways they do -- but in other ways they end up on a different "level" than the one on which they started.  So if you could somehow follow the Alice string around the branch point, you end up back at the same point in space-time... but "somewhere else".

[Technically:  Represent the universe by a covering space/Riemann surface covering type dealie.  The "apparent universe" is the base space, and a "space-time co-ordinate" is a point in the base space.  A "point of space-time" is actually a point in the covering space, however, while the "collection of points for a given space-time coordinate", aka "a point of global space-time" is really the fiber of the co-ordinate in the base space relative to the projection from the upper space.  Finally, the "(local) universe of a point", I guess you could call it, looks like a lifting of some neighborhood of the "space-time coordinate" in the base space.  For the logarithm example I gave above, the base space looks like C, the upper space looks like the Riemann surface of the complex log function (a giant bi-infinite planar corkscrew, fwiw), and a maximal local universe looks like C \ a branch cut for the log function.]

Quote

Originally posted by Lil:
I still say that parallel time lines/realities/universes *whatever you want to call it* is far more inconsistent with the Dromverse than a single time line *even* if it means you can change the past.

I tried to use a single-universe model to explain Ouroboros -- insert obligatory at the recollection of that magnum opus :crazy: -- but it seems pretty clear to me that multiple whatevers are now required to make the Drom universe consistent.  The idea here is to construct a universe such that the one subsumes the other, not just replaces it; how successful it is, of course, depends on... well, hell, it won't be successful.  I guess the best I can hope for is "vaguely mathematically plausible" :)

- Anarch
Still awaiting Orpheus' treatise on the subject...


#47 Cardie

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Posted 31 January 2003 - 04:19 PM

Una Salus Lillius, on Jan. 31 2003,10:22, said:

I still say that parallel time lines/realities/universes *whatever you want to call it* is far more inconsistent with the Dromverse than a single time line *even* if it means you can change the past.
We're getting a fudge of the original Dromverse philosophy either way. However, since the big point of ADDB was that you can't erase what has already happened, making things happen in two different ways in parallel seems to me less of a violation than suddenly saying that you can erase one timeline and substitute another.

BTW I thought of a way that TUM could sort of occur if there were only one timeline and the tesseract events only allowed trips backward and forward along it. Not quite as angsty or heroic, put permit me some fun:

1. It's the Battle of Hephaistos. We see Rhade heading into an escape pod and leaving the Andromeda. Just as he is about to clear the black hole, he is caught in a time dilation.

2. Two years before the date on which the Maru pulled the Andromeda out, Rhade's pod escapes the pull of the event horizon on its own. It is brought on board a small Nightsider vessel hired by Gerentex. Gerentex has come to scout the black hole, because he's sure that the Andromeda is in there somewhere, a treasure waiting to be plucked out. Rhade, after getting over the shock of the missing 300 years, assures him that the ship was sucked into the black hole--he sabotaged it himself. Gerentex is sceptical but agrees to drop Rhade off on the Jaguar home world.

3. Bolivar welcomes Rhade with open arms--they have a common grandmother 10 generations removed. Bolivar offers Rhade one of his sisters, but Rhade sees how the marriage of Beatrice and Cuatemoc is working out and says no. He also challenges Bolivar to rise above his sybaritic ways and try to restore the greatness of civilization. Bolivar finds him tiresome and a potential danger, so gives him a small ship with which to pursue his quixotic quest.

4. After months of fruitless and frustrating wandering, Rhade finds himself on Sintii, where the Perseids agree to help him recover the information lost in the destruction of the ASU. They tip him off to the existence of the ASU "special collections" librarians.

5. While he's there, he gets caught in a tesseract event. Looking for Hohne in his study, he finds himself instead confronted by a gold former pixie who seems to know all about him. She tells him that the Andromeda must be frozen in time so that Dylan can save the fallen universe. For that to happen he, Rommie and Dawn must not succeed in breaking free of the event horizon. Trance must therefore send Rhade back in time. If he kills Dawn and keeps Dylan otherwise occupied until the time dilation sets in, Dylan can survive to be pulled out by the Maru, whose crew have just been hired for the job. Then Dylan can save the universe. Rhade agrees. Unfortunately, his delaying action causes his death.

See, sometimes it's better to sacrifice temporal mechanics for high drama.  :p

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#48 Anarch

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Posted 31 January 2003 - 08:43 PM

Here's a slightly better visual image for those of you playing along at home:

Start with a (Euclidean) plane, which we'll imagine is plane C of complex numbers.  To any path p in the plane we'll associate a number that I'll call I(p).  Technically, this will be the (1/2 pi i)path-integral of 1/z along the path p... but all you need to know about it is that it's related to the logarithm somehow.  Now this I(p) thing has an interesting property:  Whenever p is a loop that doesn't go around the origin (i.e. the center of the plane), I(p) = 0.  In the model I'm trying to construct, this is something like saying that if you start at a given point in space-time, wander around aimlessly, and return to the point where you started... then you, well, return to the point where you started.  Nothing's changed.

Ah, but things get very different, and very weird, when you start talking about the forbidden point z=0, aka the origin.  [I forgot to mention -- you're not allowed to send paths through the origin.  It's totally off-limits, even though people familiar with contour integration will realize that you can finesse this difficulty since 1/z only has a simple pole at the origin and... where was I?]  See, if your wanderings happen to take you around the origin before they bring you back home... then even though you've returned to the "same point in space-time", your I-value is not 0.  Strangely enough, this obscure mathematical expression somehow fundamentally counts how many times you wandered around the origin... and while that's kind of cool in its own right, I guess, the fact that there paths with nonzero I-values really messes up a bunch of other things.

[Technically, 1/(2 pi i) times the path integral of 1/z gives the winding number of a path relative to the origin, i.e. selects the homotopy class of the path in the fundamental group of C \ {0} relative to the generator p(t) = e^{2 pi i t}, i.e. a circle in the positive direction.]

Now for various reasons we'd like to "rectify" this problem of having some paths with nonzero I-values.  The original, official answer is that it can't be done: all you can do is to restrict the types of paths you choose.  [One definition of the complex log function is basically to do just that.]  But in the 19th century, a very clever man by the name of Riemann came up with a different answer: the problem isn't the type of paths being chosen, the problem is that the function you're trying to compute (in this case, complex log) doesn't really live on the plane; it actually lives on something called a Riemann surface which, though related to the plane, has fundamental differences.  So, next post... what the Riemann surface of the complex log looks like, what branch points are, a funky picture of that mathnobabble I spouted off previously, and how this may (or, tbh, probably doesn't ;)) relate to the matter at hand.

Oh, and hee @ Cardie ;)

- Anarch


#49 Anarch

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Posted 31 January 2003 - 09:48 PM

The connection with logarithm

Simply put, we'd like to define a function whose value at any point z in the complex plane is the value of I(p), where p is any path from 1 to z.  ["1" being the point (1,0) in the plane.]  Notice that this almost makes sense... because if your paths don't mess around with the origin, any two different paths from 1 to z form a loop that doesn't contain the origin (going there along the first path, coming back along the second path), so their joint I-value is 0; and a little abstract nonsense shows that the I-values of the two paths must therefore be equal.[1]  If the joint path happens to enclose the origin, however, wackiness ensues; the loop now contains the origin, and the two values won't agree.  Pre-Riemann, as I mentioned, people solved this problem by simply disallowing certain paths; specifically, you make a cut -- called a "branch cut" -- along the negative real axis and then disallow any paths that have the temerity to cross the branch cut.  What Riemann realized was that there's a different, better way to solve the problem...  and so, without further ado:

The Riemann surface of the complex logarithm

OK, this is actually pretty easy to visualize.  Start with a disc (i.e. a filled-in circle): this will stand in for the complex plane.  Mark a dot on the center of the disc; this will be the origin.  The problem was that when you wrapped a path around the origin, something -- this "I-value" thing -- incremented.  The trick will be to make an increment of the I-value (which is a mere computational difference) correspond to a physical displacement.

So, here's how to do it:  Take another disc, again with a dot in the center.  On each disc, mark a point on the edge and cut a straight from that point to the center -- this is the physical realization of our "branch cut" -- and then bend one of the "flaps" you've just created up, and bend the other one down.  What you should get is two shapes that look kind of like parking ramps: you circle up the flap that got bent downward, past the part of the disc opposite the cut (which didn't get bent) and then up the flap that got bent upwards.

Now, the "paste" section of the cut and paste:  Place the two discs on top of each other, separated by a reasonable distance.  Glue the upward flap of the lower disc to the downward flap of the upper disc.  You now have a two-storey parking ramp extending from the "downward" flap of the first disc right the way up to the "upward flap" of the second disc.

Now, repeat this with another disc and you get something that looks like this:

http://www-math.mit....riem_log_Z.html

Notice that you can keep circling up infinitely... and down infinitely.  That sort of explains what I meant when I said that the Riemann surface for the complex log looks like a giant, bi-infinite planar corkscrew.

The key point to realize is this: we've traded a computational discrepancy for a physical displacement.  And this makes it possible not only to figure out certain essential properties of the complex logarithm -- which is v. important for some mathematical applications -- but will, in the next post, be used to illuminate what the frell I'm talking about.


[1]  I[p + p'] = I[p] + I[p'] for any paths p, p' such that p ends where p' begins.  "Addition" of paths is just concatenation: go where p tells you and then, when you get there, go where p' tells you.  The essential point in the above proof is that "coming back along the second path" is tantamount to travelling along the path -p' (i.e. p' oriented in the opposite direction), and that I[-p'] = - I[p'].  Therefore, if the joint path's I-value is 0 we have:

0 = I[p + {-p'}] = I[p] + I[-p'] = I[p] - I[p']

and so I[p] = I[p'].


ETA:  Aha!  Knew if I looked hard enough I could find it!

http://www-math.mit....ures/index.html

Not just a discussion of Riemann surfaces... but a discussion with PICTURES! :D


#50 Bad Wolf

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Posted 01 February 2003 - 12:15 AM

I don't know which to fear more:  Cardie's high drama or Anarch's high math.... :eek:

That's what I get.  :)

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#51 ArchAngel

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Posted 04 February 2003 - 08:43 PM

Ok, I'm going to throw this into the discussion without having seen the ep in question (and its mainly for Lil with regards to Rhade)

If I'm correct in assuming that things go to hell in a handbasket in TUM Rhade's universe/timeline, then a major reason why he would want to help save Dylan's universe/timeline, is that in it he has a chance to "live on" in Telemachus Rhade - his genetic reincarnation. Now according to Double Helix, that is what Nietzscheans strive for above all else. I would think that that would provide some motivation for his actions.

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#52 Christopher

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Posted 04 February 2003 - 10:11 PM

ArchAngel, on Feb. 04 2003,20:43, said:

If I'm correct in assuming that things go to hell in a handbasket in TUM Rhade's universe/timeline, then a major reason why he would want to help save Dylan's universe/timeline, is that in it he has a chance to "live on" in Telemachus Rhade - his genetic reincarnation. Now according to Double Helix, that is what Nietzscheans strive for above all else. I would think that that would provide some motivation for his actions.
Except he had no knowledge of Telemachus' existence.  All he knew was that his attempt to rebuild civilization had failed and he had an opportunity to "pass the torch" to someone who could do it in another reality.  He had no insight on the specific course of events in that reality.

Of course, he may have simply not known enough temporal mechanics to realize that his timeline would continue to exist.  He may have believed he was "replacing" it.  I mean, he was in the heat of a life-and-death crisis, making snap judgments -- not really a place to consider complex existential questions.

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#53 Bad Wolf

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Posted 05 February 2003 - 02:31 AM

ArchAngel, on Feb. 05 2003,01:43, said:

Ok, I'm going to throw this into the discussion without having seen the ep in question (and its mainly for Lil with regards to Rhade)

If I'm correct in assuming that things go to hell in a handbasket in TUM Rhade's universe/timeline, then a major reason why he would want to help save Dylan's universe/timeline, is that in it he has a chance to "live on" in Telemachus Rhade - his genetic reincarnation. Now according to Double Helix, that is what Nietzscheans strive for above all else. I would think that that would provide some motivation for his actions.
As Christopher points out, Geheris has no knowledge of Telemachus Rhade, which makes his sacrifice both more poignantly heroic AND less comprehensible.

Not that Ash and Zack intended to leave us with any complicated issues.  Nope they'd NEVER do that....;)

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#54 Cardie

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Posted 05 February 2003 - 04:56 PM

I think it was faith that he could take no action in the future that would more profoundly alter the shape of the universe, and in the direction that he ultimately wanted it to bend. Whether he was there to see it unfold was immaterial. Only he could establish the Dylan timeline that had the better chance of remaking the fallen universe.

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#55 Cardie

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Posted 05 February 2003 - 03:37 PM

Una Salus Lillius, on Feb. 05 2003,02:31, said:

As Christopher points out, Geheris has no knowledge of Telemachus Rhade, which makes his sacrifice both more poignantly heroic AND less comprehensible.
But Rhade here is an existential hero. He knows that he can create a timeline that may arrive at a better place than the one he's currently on. This is an incredible act of will, whatever the personal consequences. Indeed, it becomes less rewarding on the existential level, the more you know that there are compensatory rewards. I see the birth of Telemachus as the universe's payback to Rhade for shaping it to the good without expecting any good for his action in return. It's kind of like the story of Abraham. If he made to sacrifice Isaac because he always figured that a benevolent deity would stop him, he's not be a spiritual hero. Isaac is spared because Abraham was prepared to give up his beloved son and his promised destiny to be the father of a great nation.

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#56 Bad Wolf

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Posted 05 February 2003 - 04:28 PM

So, you see his sacrifice as the ultimate leap of....


FAITH?

So the next question is:  how Nietzschean is that?

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#57 Cardie

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Posted 05 February 2003 - 04:33 PM

Though I used a religious anthology, it's the ultimate leap of faith in the power of the individual will rather than in the Divine, but it works in a similar way and is very Nietzschean in the truest sense--although I think Rhade was also channeling Kierkegaard at this point.  ;)

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#58 Bad Wolf

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Posted 05 February 2003 - 04:41 PM

I don't know.  Was it faith in the outcome of his last assertion of his will?

Was it faith in the universe to do right by him if he made the sacrifice?

Or a mixture?

Hmmm.

I may have to watch this again....:)

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Quote

Quote

(Una Salus Lillius @ Feb. 05 2003,16:28)
So the next question is:  how Nietzschean is that?

I think the whole point of Rhade is that he's not a stereotypical Nietzschean.  Like any person of true intelligence and character, he chooses, interprets and adapts his beliefs according to his own judgment and experience, rather than just blindly following a dogma.  And the point of TUM is that there's more than one way to be Nietzschean -- that the Nietz's we've seen represent the prevailing attitudes of the post-Fall era, and that Nietz's in a different time and context could be different in their values and behavior.  (This is one of the overlooked strengths of Enterprise -- the way it's made a point of giving 22nd-century Vulcans a distinct culture, allowing the Vulcans to be a credibly dynamic culture rather than just reducing them to an essentialist stereotype unchanging over time.)
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Posted: Feb 5 2003, 10:12 AM

Quote

Well this gets into all kinds of thorny questions (my favorite kind).
What is a "stereotypical" Nietzschean.  And isnt' what we should be talking about when we talk about whether a course of conduct is "Nietzschean", the "ideal" Nietzschean and what is that?

Edited by Christopher, 04 March 2003 - 05:32 PM.

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#59 Orpheus

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Posted 25 February 2003 - 11:49 PM

I wish I'd been around to chip in earlier, rather than throwing in my random thoughts at the end. I may seem to be repeating stuff others said, but (unless I accidentally overlooked something), I  always add a twist that (I felt) had important consequences.
(more thoughts will follow. This post is already too long)


PARALLEL (BRANCHING, DIVERGING) UNIVERSES
I think that the "Many Worlds Hypothesis" [MWH] is the only sensible resolution of the eps to date. Basically MWH interprets Schroedinger Cat to mean that rather than 'reality' being a waveform of "50-50 live or dead cat", we can only generate a hybrid equation with two possible outcomes - two otherwise identical branched universes: one with a live cat, and another with a dead cat. It's impossible to know which one *YOU* are in until you open the box. "Reality lottery: scratch the wax to see if you're a winner" Meanwhile, there is another you in another universe, making the opposite universe.

Such hybrid equations are quite common in advanced sciences. In chemistry or particle physics, for example, we often calculate hybrid states when we can't directly calculate a property we don't fully understand. Most of you have heard of aromatic compounds (like benzene) which are more stable than you'd expect; aromatics are just one example of a larger class of "resonance structures" where there are two or more allowable alternatives (e.g. bond structures) and the actual observed behavior suggests a mixture with some of the benefits (or partial energy contributions, etc.) from each allowed state. In reality, there isn't a mixed state, but a different state that is *approximated* by mixing the states of simpler theories.

This (to many scientists) makes the role of the observer less 'mystical'. The Observer doesn't FORCE the Universe to assume one state or the other by collapsing the Schroedinger wave; s/he simply OBSERVES the wave and LEARNS which branch s/he is in. In another branch, an identical observer is making the opposite observation.

MWH isn't quite as tidy as I make it seem (or it'd be universally accepted). The underlying quantum event wasn't the death of a cat - that was just an amplified effect for the student's benefit. The quantum event is the decay of an atom -- so the MWH would spawn new universes every time any of its atoms decayed (or failed to decay) This leads to all sorts of potentially messy speculations like quantized time, etc.

This is as good a time as any to toss in the idea of "reinforcing branches". The Romans had a maxim that "A difference that makes no difference *is* no difference" (later a basic legal principle: De minimimus non curat lex") In the case of Schroedinger's Cat, the atom could have decayed at any nano-jiffy during the time the box was sealed - the cat would be equally dead. Each nanojiffy when the atom could have decayed should have spawned a universe split, but all othose uncountable nanojiffies would add up to two distinct ourcomes. We can consider them to have merged.

I mention this because under strict MWH, evach atom in the universe has some probability of decaying in every nano-jiffy (even a single proton, H-1, whose half life is longer than the expected life of the universe, still *has* a half-life, and hence, a chance of decay) This means a universe where EVERY SINGLE ATOM simultaneously spawns a parallel unierse every nanojiffy. Our perceptions (and probably our math) would merge all the branches that made no difference, jusI as we merge allowable alternative chemical structures to approximate resonance structures.

A MATTER OF SCALE AND THE SCALE OF MATTER
I believe that Rhade's scar was deliberately intended to PROVE that there were different branches. Rhade I never had the scar (he died without killing -or meeting- tyr). Only a mismatch between Rhade II and Dylan I could result in the opening scene we saw.

Instead of looking at it on a human scale, let's look more closely. Let's say Rhade ate a hot dog just before the UTN Battle Drill. Where are the atoms of that hot dog at the end of the episode? To Rhade I (who was probably tossed out an airlock to avoid confusion), 100% of the hot dog atoms are in his belly, but to Rhade II, some of the atoms became, and probably remain as, part of his tissues. If Rhade I and II were from the same universe (branch) the same atoms would have to be in two places at once. If they are from different branches, there's far less paradox, because the nature of branching reality is that every single particle is 'cloned' at every branch.

[This is one part of the MWH that give some physicists headaches]

If you look at TUM (or ADDB, Ouroboros, etc.) on any level other than a human scale (plotline), you'll find paradoxes in every theory I've read or considered thus far, except MWH.

RHADE II'S MOTIVATION for "SELF-SACRIFICE"
I understand Lil's reservations, but I think I can answer them: Rhade II hasn't been fighting for "his own" universe branch since ADDB. When he "changed the past", he was actually transiting from one branch (events as they would have happened without Trance's time-piloting) to another

If Rhade II hasn't been in his original timeline branch for years, how can he justify his all his struggles? How can he continue? He must decide that whatever branch he is experiencing in the "real" one to him. It's a tricky point, but necessary under MWH. It's also very pragmatic. We ALL live our lives as we experience them, with no regard for any abstract quantum theories that may underly them. The 'real' universe for anyone who jumps branches is the one s/he experiences at a given moment, not the one where they were 'born'.

But if you ask me, there WAS a gigantic plot hole, which some of you have heard me bemoan for weeks: Why would Rhade have to die at all? Why couldn't he remain alive and help guide Dylan through the politics (if not the pitfalls) of the coming years? The reset (changing the identity of a central historic character from Rhade to Dylan) will send Rhade -and Trance- back to Square One as far as RECALLING specific events is concerned (the slightest change has cascading efffects), but Rhade still has very helpful knowledge about the state of the Post-Fall universe.

TRANCE AND THE EXPERIENCE OF TIME
A lot of what I've said about the experience and pragmatic approach to time doesn't apply to Trance, who clearly experiences both time and alternate branched universes differently than we do.

We've seen that Trance can forsee (to a limited degree) alternate branches. Her limitations are what make her (and her plight) interesting. I think this could have been handled a bit better over the course of the series. I'll concede that it was handled quite well sometimes, but... 'nuff said.

I just wanted to throw this fact into the mix. I won't speculate further on the exact nature of her abilities or limitations, because  the bonsai in TDB was a metaphor for something we can't directly experience (certainly not on a 2-D TV in a mere 42 min) Therefore, one must be cautious in interpreting it.

THE RIGHT HORSE -er- TOOL
No, not the episode, the concept. As far back as ADDB, I speculated that Trance (or the group she represents) could tweak events to bring together the 'right' Tyr, the 'right' Beka, and the 'right' Harper for maximum utility, drawing from similar but not ientical universes. For example, I used to make a minikit -a mix of metric/inch sockets, and other random parts that happened to be most useful for a given car (at one time, cars sold in the US were not 100% metric, but used many metric parts)

In ADDB, each character seemed to have a slightly different recollection of the Battle of Witchhead nebula. This is completely understandable, given their differing backgrounds, and the general collapse of civilization. However the same 'excuse' could cover a wealth of mismatches. The crew might be collected from different branches, and never realize it. There are so many little moments that could tie into this. Sid's message to Beka (TPTWHE) was lost in the mail for three years, yet Beka still showed up at a pivotal moment -- this is just one of many coincidences that might make more sense if Trance (or someone) re-ran the timelines, trading in a mix-and-match piece, if the existing crew seemed to be a bad match, or tweaking things slightly, so that genuine coincidences served a purpose in the Grand Plan.

Let me say right now that I think Trance was Forecasting in

In TUM, I think Trance decided that Rhade was just the wrong tool. Sometimes you can get a nut off with pliers (hey! no comments on my sex life). Pliers are more useful in general situations, too, but a wise temporal mechanic will abandon the pliers for a less versatile wrench before he strips his nuts.

I'd forgive A LOT if Dylan's praeternatural knack for doing the right thing (however far-fetched) actually came from being dragged back and forth through time a few thousands times, exploring different alternatives. Maybe Dylan was less "The Chosen One" than the most convenient possibly suitable candidate who happened to be on the ship which happened to get time-dilated at Hepaistos. Then Andromeda truly is the star of the show on a pandimensional scale.

Then Captain Terrific can be a joe - in many ways an impressive joe, but nonetheless, just a guy instead of a superhero. Many of the traits that we criticize would make perfect sense. Remember Crazy Dylan? I actually started to make sense - more sense than any ultra sane Captain Terrific would have been. Wisecracking and glib Dylan might make perfect sense if he's -not quite a puppet, but a player- who's been dragged back and forth though successive iterations of critical junctures of time until all the coincidences lined up and an acceptable answer 'just fell out'.


HOW "GLIB DYLAN" COULD BE A STROKE OF LITERARY GENIUS
Think about it: if the time-looping is perfect, Dylan's experience would be: jeez, ever since Hepaistos, things just work out, no matter how off-beat my ideas seem even to me. Heck, sometimes I do things on whim that are clearly against all my training and judgement, and they turn out to be strokes of genius. What gives? (He wouldn't know he'd gone by the book 1000 times and failed.)

Generally, SF always posits some trace after-effects from successive iterations of a time loop. While you might argue some sort of Heisenberg effect, it's really just a literary necessity: "Groundhog day" would be boring if no one noticed the loop. In a formal sense, Trance performs the role of 'the observer' (even if we rarely see how event look from her perspective), but an incidental effect (a once-earnest Dylan becoming glib and finding it almost impossible to take hos won predicaments seriously) would not only make sense, it would be almost inevitable, if Dylan's only surviving memories were of the times he did something rather silly -- and it worked anyway.

At any given critical juncture, Dylan would have a handful of sensible by-the-book responses. In many cases those would be dead-ends, repeated thousands of times, and ending in failure (His most dangerous enemies would typically be able to foresee the sensible reactions and plan for them) Therefore, a disproportionate number of his "great plans" would be random slap-happy moments of not caring -- and to him, this would seem to work (whether he liked it or not!)

In "normal life" slap-happy actions tend to fail or get you killed, and sensible decisions tend to work. But this isn't normal life, 'getting killed' isn't the end of the game, and only successes are remembered no matter how silly the action that produced them. It'd drive anyone nuts. Ladies and gentlemen, Logic has left the building

I happen to believe that Trance was projecting (predicting) in TDB,  rather than genuinely rewinding time, but if you add in ADDB and the other shows, then re-iterating a critical patch of time isn't out of the question.

I mention this because I think it's a unique, but quite inevitable psychological effect on a character in this kind of "Repeat until it works" scenario. I don't seriously think this is Dylan's situation


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