Actually, Cysero solved the problem by returning the seven extra Bacon Orbs, before he himself came to get each one of them. It would probably have ripped a hole in time if we had lost our battle against SMUDD though, because then we'd have lost all the orbs...
What comes into play here is which order he returned the orbs in. Since they're indistinguishable, and they were merged into a single orb... but they're not interchangeable.
Previously I determined that, provided the first and last orbs were in the right place, the orbs in between would reorder themselves in such a way that there was no paradox. Hence the probability wasn't quite as low as I originally though, but it was still 1 in 8*7 (as opposed to 1 in 8!, or 1 in 8*7*6*5*4*3*2*1)
I suppose that definition may apply, but I see nothing contradictory about the scenario. But that's subjective. Not being swayed by common sense and all that...
and yes, a bootstrap paradox DOES go on towards infinity. besides, there's an infinity at BOTH ends of the number line. positive AND negative.
A bootstrap paradox recurs infinitely.
The nature of any particular number line is irrelevant here. What we're dealing with is a countable infinity. It's been brought up in previous discussions, before you'd have been around I believe; the mods weren't too thrilled with how mathematical things got though, so I'll keep it simple. (Actually, if anyone has a copy of that post, or a link to an archive, I would appreciate it; I lost my copy when my PC imploded).
There are multiple types of countable infinities. Some deal with n values (the number assigned to each iteration) of only the natural (positive) numbers, while others deal with both positive and negative ends; these two types of infinity are mathematically incomparable.
*looks around fearfully for a mod
Say we take a scenaro in which someone is the first time traveler. Clearly, linear causality led up to their existence. This is timeline A.
They travel to an earlier point in timeline A, and change the events leading up to their travel of time. This is timeline B.
Timeline C is when the influenced person travels...
And eventually you get timeline n, which is equal to timeline n+1. This is the point where every timeline is identical to the next (within whatever arbitrary range satisfies you).
Timeline A is the origin. It is not infinite; in fact, there is no timeline preceding it. Since timeline A leads to its own modification (and the creation of timeline B), timeline A is the first.
Clearly, we're dealing with a countable infinity with the nth iteration being a natural number.
If we assume that two timelines-- that are so close that the differences are irrelevant-- as identical timelines, we find that there are actually a finite, though astronomical, number of events that can occur.
Or, in mathematical terms,
If we accept that timelines n and n+1 are indistinguishable if every particle in them is within a certain, miniscule range of each other, then no matter how small the range is, our potential timelines are not infinite, as we've just reduced the event space to a finite number of events. They shift from being infinite to simply becoming astronomical.
And, of course, to reiterate, the bootstrap model makes certain assumptions about time travel, in that it operates in a simple, macro-scale feedback loop. This isn't necessarily true.
I have a number of explanations of different things that could happen, but they're all complicated, and probably unintelligible to most members.