Frank/Donnie causal loop paradox

[Bigboy]

I was scooting around the IMdB and someone bought up a question that I hadn't seen asked before, so I did a search of this site - it has been asked here but never answered.

Here it is (Credit to Guest Drew):

"Doesn't frank already have to be dead to come back in time to tell Donnie about the engine? For instance, if Donnie didn't move from his bed the night Frank told him too, than Donnie would've died. But in order for Frank to have done that, Donnie would've had to live past that night to kill Frank so that Frank could go back in time to tell Donnie...make sense?
Isn't that a paradox? Donnie should've died that night, but Frank saved him. This was allowed only because in the future Donnie kills Frank, but without Frank's intercession, Donnie would've died and he would not have been able to kill Frank. "

This is totally consistent with the multiple universes view, as the causal loop he describes takes place etirely in the TU.
The established causal loop (MD Frank saves Donnie, Donnie kills ML Frank, ML Frank becomes MD Frank, Repeat) is logically consistant and stable, but the paradox lies in establishing the loop - it's like the chicken and egg problem; which came first?

Adding an omnipotent God and/or fate into the mix simplifes things (but I personally don't like those ideas), so any thoughts?

[Bigboy]

OK - this has been left to hang for a while, but I think it's interesting enough to look at further.... (HA! I would say that - it was MY post! ;D)


Anyway here's a diagram showing MD Frank's TU cycle:



This loop seems causally stable, but the apparent paradox is that the loop seems to have no beginning - so where did it come from?

Not necessarily a paradox:

A loop like this with outside influence won't be doomed to repeat the same actions each time around the loop. Past faliures will allow the Mover to modify and refine his manipulation - so the Donnie/Frank Loop can be modelled as a feedback loop, like this:



i = input. This is unchanging, and represent the state of the TU at the point before the engine hits Donnie's house.

o = output. This is the state of the TU when ML Frank is killed and MD Frank is created.

f() = A function of some kind. This describes how the TU changes (is manipulated) between 'i' and 'o'.

g() = Another function. This describes how MD Frank going back in time will affect the immediate state of the TU

e = Really put there to make the sums easier, but represents the state of the TU just after MD Frank appears.

The circle thingy represents a combination of inputs (basically just adds them together then spits them out). This represents the moment MD FRank first appears.

The functions f() nad g() would, in reality, have to be stupidly complicated to model the intricate manipulation of the TU - but for this I'll make them dead simple:

f(x) = N.x ; N<1; N>0
This just means "multiply by N, where N is between 0 and 1".
The idea here is that The Mover wants to constrain actions within the TU - limit the value of 'o'.

g(x) = -x
This just means "Make Negative".
The idea here is that the Mover does not want to repeat any faliure, so MD Frank immediately constrains the TU's possibilities even further.

OK - some quick algebra:

A) e = i - o
B) o = e.N

substitute A into B:
o = (i - o).N

Multiply out the brackets:
o = i.N - o.N

Group outputs (o) :
o + o.N = i.N
o.(1 + N) = i.N

Show the vaue 'o' in terms of 'i':
o = i.(N/1+N)
This o is how the TU turns out given the way it began (i) and the effect of the feedback loop.

So now we have an output value o - BUT the output doesn't suddenly jump straight to that value as soon as the input hits the loop: if we follow the values round the first loop we can see that the input hits the "adder", but there is nothing to add, hits the first box and the output is i.N instead of i.(N/1+N).

If we give i and N a value its easier to see:

Say N = 0.5 and I =1;

Loop	input i	e	output o
0	1	1	0.5
1	1	0.5	0.25
2	1	0.75	0.375
3	1	0.625	0.313
4	1	0.688	0.344
5	1	0.656	0.328
6	1	0.672	0.336
7	1	0.664	0.332
8	1	0.668	0.333

(Predicted value o = i.(N/1+N) = 1.(0.5/1.5) = 0.333)

If we graphed the output over time we'd get something a bit like this:



The important bit is the "wobble" before it settles to a stable value: If we imagine that each value of 'o' represents the outcome of a different history of the TU within the loop, and that the eventual steady value of 'o' is the out come we see with Frank's seemingly impossible loop, then it no longer looks impossible - many histories were "tried out" before settling into what we see - the only condition that had to be met in each one was that Frank had to die, but not necessarily by Donnie's hand. In fact Donnie needn't even survive the original impact in these transient histories (in the first it's virtually impossible - no Frank to save him!).

I put "(abstract)" under "time" on the graph, because it doesn't represent Time in the sense that we experience it. As far as tangible reality is concerned there is one history of the TU, (indeed there is only one instance of the TU, and everyone in it only experiences one course of events).
Time on the graph is really the transition through some higher "state space" of possible TU histories - the only one that ever becomes "real" is the steady, stable one we see.

How all this manifests itself to the outside observer/manipulator/the Mover (God/Scientists/Aliens etc), I haven't a clue (would they remember each incarnation of the TU history? maybe), but I think it explains away the only real paradox of the movie.

(Massive edit!)

[Bigboy]

^ Edited.

Images fixed, sign error corrected and is hopefuly easier to follow (knowing me probably not... )

[greedy]

still stuck on a^2 +b^2=c^2

[Bigboy]

Good thing there are no triangles in there then!

[greedy]

after reading that i hd to get drunk to bring my brain back on kilter

[greedy]

i had to exalt you for thi post

[MoonageDaydream]

This is quite impressive.

[Matt]

*Subconscious Frank* doesn't add up to me. He seems to transcend the logical rules of time travel. His existence depends on an action he has to set in motion. And if you don't exist in the first place, how can you trigger a chain of events.

Unless you're a time tyrant and the anti-hero of the entire film.

Maybe Frank's kind are just looking for a living receiver that doesn't have the guts to kill themselves and the tyrant within them to destroy the universe.

Subsconscious Frank is the enemy of fate!

[FrAnK]

great job Bigboy. I read everything.you got the formulas right. A+!

[Bigboy]

you got the formulas right. A+!

Lol. Thanks!

[elizabeth]

It's really something to think about..
When the POTT describes the TU as unstable and that it will eventually collapse upon itself,could this paradox be the thing that causes that collapse??

[terabyte]

Holy crap BigBoy, that's amazing. I wish I would've payed attention in algebra more so I could understand it more. But I'll give it a look later when I'm more awake.

[Reed]

Rather than do the math, I guess you're just saying it's like that episode of Star Trek the Next Generation when they keep looping in time until they figure out how not to get blowed up?

[Bigboy]

Not as such - I'm not saying that events repeat at all, rather that MD Frank's manipulation forces a traversal of TU state-space (a higher dimensional space that contains all possible histories of the TU), until a stable positive history is settled on.

It may just be a matter of semantics between the pure logicial loop I present and an actual manifest repeating time period; I'm not sure.

It's also worth noting that this 'loop' does not constitute the entire TU - that it the TU itself is not a loop.

I've kind of moved away from this anyway in favour of the idea that MD Frank exists retrocausaly (ie backwards in time). (See Here