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Old 2013-03-01, 16:31   Link #31981
theacefrehley
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(Kinzo not meeting Beatrice was just an example of rare events)


Why, among infinite possibilities, some possibilities can't be finite?
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Old 2013-03-01, 16:49   Link #31982
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Originally Posted by theacefrehley View Post
Why, among infinite possibilities, some possibilities can't be finite?
They can be, if they're impossible.

No one can give me a single good reason why tragedy must happen though. Because no one can, because that's ridiculous.
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Old 2013-03-01, 17:16   Link #31983
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They can be, if they're impossible.

No one can give me a single good reason why tragedy must happen though. Because no one can, because that's ridiculous.
And it's not so easy to make something 'impossible' when we're given an infinite amount of possibilities we can twist in past history to turn that fact 'possible'.

It can simply be hard as sometimes there are just too many variants we've to change and a mistake might lead us back to square 1 or in a worse option.

That's not Yasu/Lion's case though.

His story is sad because it's mostly also due to misfortune, to coincidences leading to the worst outcome.

Have Natsuhi not go out for a walk or the maid not following her and Lion won't fall from a cliff.

Nowhere is said that Natsuhi HAD no other option but leave and the maid HAD no other option but follow.
It was a matter of casual choices, same as it's Beato 2's death.
Rosa might have not found her and she might have not slipped therefore Lion might have remained with her and grown up to become a variant of the Beato we see in Ep 8...
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Old 2013-03-01, 17:22   Link #31984
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Yeah, but that's the thing about infinities.

There are fewer worlds in which Kinzo and Beatrice never meet than worlds in which they do meet. !Beatrice < Beatrice.

However, there are infinite worlds in which they meet, and infinite worlds in which they don't. !Beatrice < Beatrice still holds, but it's just "the set of infinite possibilities in which x happens is greater than the set of infinite possibilities in which y happens."

Based solely on the parameters selected by Beatrice, the beginning state of her stories is always the same pseudo-Prime state in which Kinzo did meet Beatrice, the gold was found by Yasu, etc. In Beatrice's reckoning, the chance of a world in which Kinzo and Beatrice never met is zero, because she's self-selecting only worlds where that was a necessary component of her history. So for most Rokkenjima stories, it would be pointless to theorize about a world where Kinzo and Beatrice never meet, because it's irrelevant.

The problem comes in when you start looking back and making changes. Nineteen years is a hell of a long time. Even if we accept that the chance of Lion being accepted is one in a billion, that only means there's one Lion Fragment in the case of a billion Yasu Fragments. But there aren't a billion Yasu Fragments. There are probably, or could probably be, uncountable trillions, or effectively an infinite number. By that logic, there is a set of infinite Lion Fragments one-billionth the size of the set of Yasu Fragments.

And you're telling me there's never going to be happiness in any of those? Very unlikely things are certainties given enough monkeys flailing at typewriters. And if the Fragments actually reflect stories genuinely written, then it only takes one kind-hearted truth-seeker to create something that cannot be attacked. We know people like that exist (Will appears to represent them, or at least one of them). It only takes one more step.
I knew I've heard this kind of logic somewhere before.

It's similar to Cantor's uncountability proof, the cardinality of continuum in set theory.
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Old 2013-03-01, 18:29   Link #31985
theacefrehley
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But is it stated anywhere that each possible world must have necessarily an equivalent fragment/kakera in the sea of kakeras/fragments?
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Old 2013-03-01, 18:48   Link #31986
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But is it stated anywhere that each possible world must have necessarily an equivalent fragment/kakera in the sea of kakeras/fragments?
No, but why wouldn't they?
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Old 2013-03-01, 19:26   Link #31987
theacefrehley
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No, but why wouldn't they?
I don't know
Because it's a possibility There are infinite fragments, but not all we can imagine is there

Why would they, necessarily?

And how could in-fragment characters like Lion know how the sea of fragments works, to be able to call Bern' bluff?
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Old 2013-03-01, 21:37   Link #31988
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Originally Posted by theacefrehley View Post
I don't know
Because it's a possibility There are infinite fragments, but not all we can imagine is there

Why would they, necessarily?

And how could in-fragment characters like Lion know how the sea of fragments works, to be able to call Bern' bluff?
We don't know how the sea of fragments work so we can theorize everything about it, I'll give you that.
However if we go with 'everything is possible' than reasoning over it is pointless.

Ryukishi showed us that each fragment seemed to match a story. Logically one would expect that each story will have a matching fragment.

As an infinite number of stories can be generated the sea of fragments must be infinite.

Now apparently Bern herself put some limits to her sea of fragments as it has to contain fragments that include the Rokkenjima incident.
Why is this?
We know she can't find a fragment in which Ange's family will return back to her.
We know Battler must be 'dead'.
We know there can't be a happy ending.
However it's also said that Battler can win and go back by some other Ange.

So a whole bunch of fragments with a happy ending must exist somewhere... but it's of no interest whatsoever to Bern who's searching only for fragments with the Rokkenjima incident, or for Ange as that part was already 'written' in her fragment as having a sad ending.

We also can assume only a fragment can match exactly with what happened on Prime making all the other fragments 'fictional' compared to Prime.

Again, it's possible to create infinite tales about the Rokkenjima incident but let's say that the finite number Bern gave is the number of the tales created in the moment she's speaking, which must be finite.

In this way Bern didn't lie when she said there's a finite number of fragments and that they all ended in tragedy and only 1 contained Lion because what she truly meant was 'there's a finite number of tales about the Rokkenjima incident, only 1 involving Lion'.

This is possible and would make logical sense and would allow Bern to be honest and truthful.

However her truth is really easy to destroy.

We know that truths of the future overwrite truths of the past so ten minutes after she said so we could have more than 50 tales containing Lion because forgery authors just fell in love with the Lion's idea and all of them will lead to a sad ending because forgerers are writing about the Rokkenjima incident and aren't interested in a happy ending.

To be honest all this is of no interest to Ange. In truth for her only 1 fragment is important, her own and in her own the Rokkenjima incident is a fact of the past and she can't undo the past.

To Clair/Lion however things are different as the Rokkenjima incident is a fact of the future and this means in front of them there should be infinite possibilities, expecially for Lion who... well, didn't exist in Prime but in something parallel to it.

To say they can't reach a happy ending Bern would pratically forcing a temporal truth of the future on them. This however would require Bern to know the full truth on Rokkenjima so that she can say with confidence that Yasu/Lion died and didn't manage to escape and forget everything as it happened to Battler.

Honestly I doubt she knew what truly happened to Battler so her words were pure bullying using misleading information.
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Old 2013-03-01, 22:15   Link #31989
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Quote:
Originally Posted by theacefrehley View Post
(Kinzo not meeting Beatrice was just an example of rare events)


Why, among infinite possibilities, some possibilities can't be finite?
Because that's how infinity WORKS. If something is possible at all, then it will happen infinite times no matter how many times you keep going.

For there to be infinite possibilities is like saying that the dice never stops rolling, ever, no matter what. So even if we have a special die so that certain numbers come up more often, like saying there's only one 1 but 100 0's on the dice, then there's going to be 'more' 0's than 1's, but YOU'RE ROLLING FOREVER, so there's going to be an infinite number of 1's too. No matter what. It just means that those 1's are outnumbered, and are probably spaced farther apart.

Quote:
Because it's a possibility There are infinite fragments, but not all we can imagine is there

Why would they, necessarily?
Because in an infinite set, everything that is possible occurs, no matter how unlikely. The only way a fragment cannot exist is if the fragment is 100% unable to occur under any possible arrangement of circumstances.

Otherwise it's not infinite. It's just a whole bunch.

Quote:
And how could in-fragment characters like Lion know how the sea of fragments works, to be able to call Bern' bluff?
High school mathematics. Bern already stated that the sea is full of infinite possibilities.

Quote:
We know she can't find a fragment in which Ange's family will return back to her.
No we don't. Lambdadelta implies the exact opposite, actually, that Bern could look for one and deliberately not find it.

Quote:
We know Battler must be 'dead'.
No we don't. Infact, we distinctly know otherwise since in Lion's world Battler doesn't return for some reason, so he'd escape the tragedy unharmed.

Quote:
We know there can't be a happy ending.
Again, no we don't. Battler's EP8 gameboard proves the exact opposite, really.
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Old 2013-03-02, 00:26   Link #31990
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Well, let's see what the actual text says, shall we?
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Old 2013-03-02, 00:28   Link #31991
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Sooooooooooooooooooooo, yeah. The only thing restricting stories are particular parameters set or the limits of imagination. So either tons of happy Fragments exist but just don't meet the parameters of anyone in the story who searches for them, or happy Fragments can only exist if someone imagines them... and given what Featherine says in Dawn about the number of Endless Witches growing with time, this seems to be inevitable.

Bern's claim to Lion is the only statement that suggests the certainty of tragedy, and we know that Bern is a manipulative bitch who is perfectly willing to selectively filter her searches and use half-truths to torment people. Literally everything else implies that infinite means infinite.

Moreover, if we include Featherine/Ikuko's statements about writing (which I did not, but they exist), it pretty much confirms that fiction can create infinitely. The only thing that restricts Beatrice's stories is her own intentional setup of the catbox. This allows her to create an infinite space in a finite reality (Prime). If we ignore this rule and start going AU, nothing can possibly stop us from doing whatever we want.
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Old 2013-03-02, 00:37   Link #31992
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Theory: There is literally only one "Tragic Lion" fragment, which is why finding it was a miracle. But Will destroyed it. This made Lion's happiness into a certainty, which is why Lambdadelta became Lion's guardian and was suddenly a complete bro.
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Old 2013-03-02, 00:49   Link #31993
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Plus there's the fact that the end result of each kakera must agree with the observed result in 1998 in order to be 'possible', so there's that restriction (though what has been said about infinity and cardinality is correct). The problem is that "the observed result" seems to be a part of the kakera too... >.> (Meaning that the world of 1998 is ALSO variable across Episodes).

I'd say that "any possible kakera must match with R-Prime 1998" except that, well, the problem we run into most of the time, that we don't frickin know anything about R-Prime. It's PROBABLY something like what we see in EP8 but who knows. But lets assume R-Prime exists, and let's say that in it maybe the Ushiromiyas all survived and there was no explosion. Then everything we have in Umineko "is not possible at all" because it violates what we are given about the true setting: everybody lives. From this point of view, the kakeras are all wrong, but they are "allowed to be considered true" from our perspectives because we can't see R-Prime and are operating from our current understanding of how the game works.

I'd liken it to Set Theory: we have elements which are sets of sets of sets... but we can't see what each element actually IS until we can see that outer-most set.
Is s[0].class = Array<Array<Array>>? Or is it Array<Array>? We can't tell until we have access to s. We can make judgments about what's allowed based on what inner-set we are in, but the very fabric of our understanding is limited to the rules of our inner-set.

Edit: Or, to put it simply, every time a new piece of information is given to us, the set of kakera which are 'allowed' changes.
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Old 2013-03-02, 00:56   Link #31994
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Edit: Or, to put it simply, every time a new piece of information is given to us, the set of kakera which are 'allowed' changes.
Can that invalidate existing Fragments, though? For example, are Legend, Turn, Alliance, and Dawn invalid Fragments? Eva dies in all of them. In fact, two are shown after we are made aware of Eva's survival. So what do we make of that?
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Old 2013-03-02, 01:00   Link #31995
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Can that invalidate existing Fragments, though? For example, are Legend, Turn, Alliance, and Dawn invalid Fragments? Eva dies in all of them. In fact, two are shown after we are made aware of Eva's survival. So what do we make of that?
Well, either Eva died or Eva lived. We already know that Beatrice's cat box changes midway through EP1-4 because Eva's life/death status after the conference changes according to different Episodes. If you're seeking "absolute truth" then either {EP1, EP2, EP4} are false or {EP3, EP6} are false. To extend the analogy with Sets I described earlier, these two sets are both elements of some larger set, and only one of these two elements is "not immediately false".

Although it's important to realize that what is allowed depends on what level you're looking from. Knowing R-Prime fully, we can see whether Eva lives or not. But by changing your parameters, you are changing what's allowed. Let's just say we treat EP3 1998 as true. Then obviously EP2 is not an allowed explanation for the Rokkenjima Serial Murders. But if EP3 1998 is false, the EP3 is not an allowed explanation for the Rokkenjima Serial Murders.
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Old 2013-03-02, 01:05   Link #31996
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But Beatrice could present both to Battler as part of her catbox, apparently. So somehow both are valid. I suppose Battler can't know what's outside, but Ange can (and Tohya can, but apparently keeps writing shit where Eva dies or something). And what about the one Battler shows Ange in ep8?
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Old 2013-03-02, 01:15   Link #31997
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But Beatrice could present both to Battler as part of her catbox, apparently. So somehow both are valid. I suppose Battler can't know what's outside, but Ange can (and Tohya can, but apparently keeps writing shit where Eva dies or something). And what about the one Battler shows Ange in ep8?
Looking back on everything, I think the Catbox Beatrice maintains is about "the Yasu story", not that "everybody dies/Eva lives/whatever". Beatrice tries to get Battler to remember the love they had, so she's spinning stories with Yasu as the culprit, and they may blatantly contradict what we know about 1998, but that's not really Beato's purpose. She's not trying to get Battler to know the "truth", so it's not unexpected that she'd show him a kakera which is false. However, those stories all satisfy "Yasu did it because she loves Battler", so she's content with telling them. So in other words, she's showing stories which we can PROVE to be wrong in their particular reference frame (after all, Eva can't die and not die). They're valid in that they represent Beato's heart, but Beato may have shamelessly grabbed them from some other quantum state

Edit: OK so I guess that means this can be taken to mean that the whole "magic doesn't exist" premise from the first four EPs is a load of shit, because it doesn't matter if magic exists or not, because Beato can just show him a kakera where "magic exists" and then he's done. So I'm suddenly not too sure...

Super-edit: I never considered this, but how do you think Battler's direct involvement in some of the kakeras affects everything? He is shown to have control over at least his own piece in-game. Or maybe Piece-Battler is only a set of eyes to gather info about the game board without relying entirely on Beato's narrative?

Anyway, let's just say Meta-Battler decides "fuck everything, I'm hiding in Kuwadorian" and does so for every game he participates in. Doesn't that fundamentally change the end result of the game Beato made? So kakera aren't necessarily predetermined as long as there is a player.

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Old 2013-03-02, 02:22   Link #31998
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Ryukishi showed us that each fragment seemed to match a story. Logically one would expect that each story will have a matching fragment.
If you want to believe any kind of story, no matter how absurd it is, yes.
If you want to restrict and say some kinds of stories do not have a fragment, why not? If Bern searched enough, would she find a fragment where Yasu is adopted by Japan's emperor?

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Because that's how infinity WORKS. If something is possible at all, then it will happen infinite times no matter how many times you keep going.

For there to be infinite possibilities is like saying that the dice never stops rolling, ever, no matter what. So even if we have a special die so that certain numbers come up more often, like saying there's only one 1 but 100 0's on the dice, then there's going to be 'more' 0's than 1's, but YOU'RE ROLLING FOREVER, so there's going to be an infinite number of 1's too. No matter what. It just means that those 1's are outnumbered, and are probably spaced farther apart.
But how can you be sure that's how the sea of fragments work?
What if that universe allowed 17 fragments with Lion and infinite tragic Yasu fragments? 17+ infinite = infinite
How do you know it's growing and growing with every possibility?



Quote:
Because in an infinite set, everything that is possible occurs, no matter how unlikely. The only way a fragment cannot exist is if the fragment is 100% unable to occur under any possible arrangement of circumstances.

Otherwise it's not infinite. It's just a whole bunch.
As I said, how can you be sure every imaginable story has an equivalent fragment?
What about an infinite set of tragic events? It's a smaller set of infinite compared to tragic+happy, but it's still infinite



Quote:
High school mathematics. Bern already stated that the sea is full of infinite possibilities.
Did she say it to them (Lion&co)? How can they be sure she's telling the truth?
What if it's a tragic universe and there are infinite tragic fragments only? Infinite =/= All
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Old 2013-03-02, 02:50   Link #31999
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Anyway, let's just say Meta-Battler decides "fuck everything, I'm hiding in Kuwadorian" and does so for every game he participates in. Doesn't that fundamentally change the end result of the game Beato made? So kakera aren't necessarily predetermined as long as there is a player.
Ange mentions in Dawn that the "magic" the two Beatrices do engraves their actions on the Fragment. One could imagine, then, that "a board with a player" is essentially "a story with an outcome determined by the input of a secondary contributor."

In other words, let's say the story is End, but Battler decides after solving the epitaph that he's going to bust Erika's skull in with a gold ingot and hide in Kuwadorian for the rest of the weekend. Whoever initially came up with the plot for End probably didn't anticipate this, but allows it.

Now we basically have two stories, End-Prime and End-Modified. One is the base, one is the version that's used as a gameboard. In theory, both are Fragments, independent of one another but extremely similar (in that, up to the moment where Battler and Erika find the gold, they're identical).
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Old 2013-03-02, 03:16   Link #32000
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Sooooooooooooooooooooo, yeah. The only thing restricting stories are particular parameters set or the limits of imagination. So either tons of happy Fragments exist but just don't meet the parameters of anyone in the story who searches for them, or happy Fragments can only exist if someone imagines them... and given what Featherine says in Dawn about the number of Endless Witches growing with time, this seems to be inevitable.

Bern's claim to Lion is the only statement that suggests the certainty of tragedy, and we know that Bern is a manipulative bitch who is perfectly willing to selectively filter her searches and use half-truths to torment people. Literally everything else implies that infinite means infinite.

Moreover, if we include Featherine/Ikuko's statements about writing (which I did not, but they exist), it pretty much confirms that fiction can create infinitely. The only thing that restricts Beatrice's stories is her own intentional setup of the catbox. This allows her to create an infinite space in a finite reality (Prime). If we ignore this rule and start going AU, nothing can possibly stop us from doing whatever we want.
I don't deny the possibility of 'Lion's happy ending'. Obviously, if you think hard enough and change key decisions/events over the last 19, or 30 years, you can achieve almost any result, endless results.

What I question is: Does any possibility/theory/development anyone can come up with result in a Fragment in the Sea of Fragments?

This Sea is Bern's workplace, a supernatural place. The inner works of it are not known.
Just someone imagining Lion persuading the family to be good guys results in a fragment with a happy ending? Does this fragment appear in the Sea for Bern to be able to find?

I want to know how to be sure of this jump: one imagines -> fragment appears


Quote:
Originally Posted by Episode 6, Ange on Magic
"...A result without an observer can possess an endless number of ways in which it might have occurred. Humans, who can't grasp anything more than a single possibility, are unable to imagine anything."
"However, people who believe in the possibility of a witch can imagine that it was a witch's prank. When that happens, the scene of the Beatrices' prank that we have just seen is etched into the Fragment as a fact..."

So Fragments are affected by imagination, basically, which also suggests that variants on Fragments are Fragments unto themselves.
Literally, this kind of means that if someone wants to believe in fantasy, a fantasy fragment is possible, with witches running around and causing incidents. (which is pointless, imo)
I think this quote is more aimend at 'interpretation'. If you want to believe it was a Witch who did it, so be it, but that doesn't make it a real and possible world, nor that it'll be possible for Bern to find a fragment like this.
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