Thursday, 6 March 2008

K-Pax, Eternal Return, Poincare

Hurly Burly has mentioned on various occasions the similarities between CTF and the final speech of the K-Pax character Prot, played, curiously enough by Kevin Spacey (what is it with Kevin Spacey and 'end of film 'talk-overs and CTF?).

In this Prot explains that the K-Paxians have been around long enough to know that the universe will expand, stop expanding, collapse back on itself and then expand again. as such we will all live our lives again. However everything will be the same, every action and mistake of our lives will be repeated. Prot says:

"Whatever mistakes you make in this life you will live through in the next pass, every mistake you make you will live through again, and again, and again, for ever."

This is a description of a scientific/mathematical principle known as Poincare's Recurrence Theorem. This has been defined as:

"For a (time-dependent) Hamiltonian system a trajectory returns to a given neighbourhood of a point given a sufficiently long (or an infinite) time."

( The Laws of Nature by Peter Mittelstaedt & Paul Weingartner, page 162 - Spinger 2005).

In simple terms this means, as I understand it, that if we live in a finite universe with boundaries then once the universe has expanded into all the available 'space' then it can expand no further and deflates back to the 'big crunch'. I am aware that the latest research from COBE implies that the universe will go on expanding forever (but if this is the case then given an infinite amount of time the universe will become so diffuse that it will cease to exist as a coherent entity).

So if Poincare's Recurrence Theorum (and Prot's suggestion) has any validity then we are back facing what I term the 'Strong Cheating The Ferryman' Interpretation (SCTF) that we all are doomed to live the same life as Nietzsche suggested in his famous 'demon' analogy (see my next posting). However WCTF (the 'Weak Cheating The Ferryman') proposes that Daemon-induced warnings and interventions can change events and as such contribute to a far more evolutionary Bohmian IMAX within Everett's Many-Worlds (Many-Minds) Interpretation.

(note my use of 'Weak' and 'Strong' - this is deliberate and reflects two other fascinating theories of modern cosmology, the 'Strong Anthropic Principle' (SAP) and 'Weak Anthropic Principle (WAP). These are well worth a posting in their own right).

If you are interested the K-PAX Prot speech can be viewed on YouTube by following this link (you need to go in for about two minutes):



9 comments:

Hurlyburly said...

Plus it's a bloody good film. Jeff Bridges has amazing chemsitry with Spacey. This may have something to do with a very similar film he had done previous to that called STAR MAN.

Go read the K-Pax books, Prots report at the end is brilliant. It's more of a warning against the downside of human nature and what we are doing to our planet. The arrogance we have as human being is one area that works beautifuly in the film, Spacey and Bridges debate about morals, ethics and laws. Spacey is outstanding, go watch it now, all of you, it has a beautiful soundtrack aswell.

Must go, got to catch a beam of light.

Anthony Peake said...

HB,

Thanks again for pointing this out. I saw the movie a few years back but never spotted the Itladian themes.

I must read the books ... together with the half million others that I have been advised have relevence to the theory. This is zeitgeist with a vengeance!

Hurlyburly said...

Did you actualy re-watch the whole thing recently then?

It's a fantastic film regardless of the refferences so always worth a watch.

"No laws no lawyers"

"You know Mark, for an educated man you really do repeat yourself an awful lot"

Isn't Spacey great? HEY EVERYONE, YOU KNOW ANOTHER FILM WHERE KEVIN SPACEY IS BRILLAINT PLAYING A CHARACTER VERY KEVIN SPACEY LIKE?

H U R L Y B U R L Y

So...

Anthony Peake said...

er .... The Usual suspects?

Hurlyburly said...

Very funny...

H U R L Y B U R L Y

(That's all the clues i'm giving you)

ken said...

"Sensitivity to initial conditions" or "The Butterfly Effect" may also account for some variation among repetitions. I don't know anything about Poincare's Recurrence Theorem but the use of the word "neighbourhood," aside from meaning that this occurs only in the UK (because if it took place in Wisconsin it would be "neighborhood"), means that the exact same starting point is not regained. The "neighbourhood" can probably be made arbitrarily small but it will always have a finite extent. This means that everything is not exactly the same in the next go round which means that things can, and will, diverge as time goes on and each recurrence will be differ -- even if we do nothing consciously different.

Of course, the downside would be if strange attractors are relevant in which case things will never be exactly the same but they will never get drastically different, either. Think of the Lorenz attractor (which is shaped very much like a butterfly). Each time around you are on a different path but you are stuck orbiting the same points. Does this doom us to the same ultimate fate every time? Or is it, perhaps, possible to make a jump to a new strange attractor and drastically and permanently alter our "destiny"?

There is a movie called "The Butterfly Effect" (I think) with Ashton Kucher. I think I caught some of it but never watched the whole thing through. I deals with reliving an event and trying to change it (I think). This is not an endorsement but just joining in the fun of throwing out movie titles of some (possible) relevance.

Anthony Peake said...

The Butterfly Effect is yet another profoundly Itladian movie that deals with many aspects of the many re-runs of the Bohmian IMAX and how tiny changes (Daemon induced or otherwise) can bring about huge changes as the 'butterfly effect' spreads out over time.

I really enjoyed the movie but it is very depressing in parts.

Hurlyburly said...

Extremely depressing to the point that i never want to watch it again.

I prefer the Jacket. Great film also dealing with these issues, i posted about this film a few months ago aswell. With a nice picture of Keira Knightley!

Karl L Le Marcs said...

YAY!!!
I have actually SEEN "The Butterfly Effect"
*mass of voices exclaiming in astonishment*
What I would say is that the original Director's Cut ending is FAR superior to the wishy-washy cinematic release ending.
Do you agree Hurly?