Applying Markov Chains to Parallel Universes


Simon Fraser University
Registered Senior Member
Markov chains arise naturally in biology, psychology, economics, and many other sciences. You can read about them in a good first year linear algebra textbook. If a Markov chain is "regular" i.e. its transition matrix is regular, then the system being represented by the Markov chain will eventually reach a steady state. That is, no matter what the starting conditions of the system, it will always reach one particular final state, given a sufficiently long time.

In science fiction movies, books and tv shows, remember the plotline where one person steps into a parallel universe--either by time travelling into his own universe at a different time (Back to the Future) or into a parallel universe where things are different (Sliders). Have you ever wondered just what types of changes you need to make so as not to alter the system significantly?

My idea is that you can make HUGE changes and it might affect the immediate future but, if our world can be modelled with a Markov chain, then down the road it won't matter a bit, the system will end up at the same state as it would have if you hadn't made those changes.

Killing your great-grandfather or assassinating a president would likely significantly alter the future--at least, the immediate future. But given sufficient time, might the system not end up the same? Think about smaller changes, like going out for pizza rather than sushi, or choosing one high school over another. Two years from now, will your choice of meal affect the state of the world? Two hundred years from now, will your choice of high school?

You'd need a stupidly large Markov chain to model the universe but I'm not seriously suggesting we do anything like that. I only brought up the Markov chains so that people familiar with them would see the link I'm suggesting here. The idea I'm proposing is that, given sufficient time, our world will turn out (generally) the same no matter the initial conditions (i.e. regardless of our actions). If we are programmed to act a certain way (as we are, through our genes) and thus the actions of our descendents are predicted to be similar to ours on a macroscopic scale, and if the system is "regular", mightn't this idea hold?

I guess in the FAR future things may end up the same no matter what men do simply because the fate of the universe will be too macroscopic to be controllable by humankind - i.e. the big crunch, or expansion to the point where all the matter in the universe is eons apart from everything else, or whatever the final state ends up being!

Just thinking out loud. Talk back.
Though I dont really understand Markov chains, you made it very clear the idea you present. And It is a very good idea. You wrote it very well. Maybe I will learn of Markoc chains in the future. Im in 9th grade. Algerbra is really easy for me and We are doing Linear Equations. Anyway, I suppose it is like the idea that......

Everything goes from a state of disorder to order. Its how Nature works.

I would agree with you, Weitzel, on the idea that no matter what you do, the planet, even the universe will be basically the same given a large enough amount of time. I think this is an essential truism for anything, the greater the time between now and when the event occurred, the less impact the event is likely to have on you. I think there are probably very few exceptions to this.

On the other hand, if everyone understood this and took it to do whatever they wanted, the consequences of their actions can be larger than the sum of their individual actions. For instance, if I stop recycling today and never recycle again, the effect on the planet is going to be very little. Likewise, if I drive an SUV instead of a compact car, the effect on the air and gas prices will be very minimal. Even my local gas station, if they treat me badly and I never go there again, it will have relatively little effect on their business. However, if everyone stopped recycling today, or everyone drove horribly inefficient vehicles, or everyone in my city avoided the gas station that treated me badly the consequences could be huge.
It's easy to reason away that what you do has very little effect, but it has always been my belief that any system of deciding what to do is not a good system unless you can say "If everyone followed my system, would I be happy with the results?" In that way, I think we all need to conscientiously do what we believe is right.
Sorry, guess I got onto a tangent. ;)
I know that the localised "Something so small it didn't hamper the world too much" scenario has already been covered in a few speculative narratives.

Although there is still certain facts that will explain "the Butterfly Effect".

Using a model that I came up with, Lets say you have an Automated Card shark (A machine that deals cards), it's rigged to a computer and deals out a card to you. You look at it, it's the Ace of Spades and it draws you to think of some Meme that you attach to the Ace of Spaces. (A small thought, like I remember winning a hand with the Ace of Spades, Or it's uncannily an Ace)

Now the trick with this machine is it deals cards from a Parallel calculation, namely through a relativity code and frequency it places a different card for you to look at in each world.

You might have seen the Ace of Spaces here, but understand that all the other cards have been looked at as well by yourself, all in parallel (At the same time) all with different Memes (thoughts occuring because of the card).

In reality the one you see will take presidence, but the other 51 cards (and possibly joker) will have an effect on your thoughts, since you have a very small amount of energy from one of these parallels leaking the memes from the parallels. (In otherwords you multiversally think, with the Ace of Spades taking presidence and the other cards overlay at a lower quanta)

In fact this experiment shouldn't be re-enacted because of the mess that it can cause due to the multitude of parallels and consecutive thoughts. But it proves that atoms are Photonic in structure. (My understanding is that Electrons/Protons/Neutrons are all catalysed by a particular method of accelerating and compressing photons which in turn makes what you see before you nothing but a hologram)

If you set yourself a goal and take different directions to get there it will have little effect, unless it takes more time, then you might miss a lift etc.
Tristan: Thanks for your comments. If you're interested in sciecne, keep studying mathematics, it will pay off.

Deus: I agree with your comments - I stayed away from morality and ethics intentionally, though those were some of the thoughts I had while writing.

but the other 51 cards (and possibly joker) will have an effect on your thoughts, since you have a very small amount of energy from one of these parallels leaking the memes from the parallels. (In otherwords you multiversally think, with the Ace of Spades taking presidence and the other cards overlay at a lower quanta)

Whoa, I didn't see that one coming. This model of yours is wacky, Stryderunknown. :) But giving every theory a chance... Isn't our universe, and every other universe, by definition a closed system? How is that energy can "leak" from one universe into another? ... Now you've gone and got me thinking about another topic, the definition of a universe... once "universe" meant everything there is, but ever since they proposed multiple universes, a universe doesn't hold everything anymore, there's more beyond it. :rolleyes:
If you are talking about real energy then the question probably is: does the law of conservation of energy apply to our universe, or only to the multiverse? So far, I think the only quantum theory stuff that I've read that deals with multiple universes upholds the LCE for our universe, that is, any matter/energy moving between universes swaps with an equivalent amount of matter/energy in the other universe.
Oh no... I just wrote this awsome reply like a page long and i hit the wrong button and it got all erased.


Carl sagan liked that idea and he called it the "Cosmos". I like to call it the "Multiverse"

But what we really need to do is to define "Multiverse".
Should it mean a cosmos in which there are many closed system universes that are all different. Or should it mean that there is a cosmos full of universes that were all the same exact thing at one point except that different paths were taken in the fork in the road ( meaning discisions or events no matter how small or big).
Hi Weitzel,

It's a good idea, but you assume that the transition matrix is constant in time (the outcome after a long time is determined completely by the transition matrix itself). However, one could suggest that the transition matrix changes if you go back in time (eg. some probabilities are no longer possible because you killed your grandfather). In the end, this would result in a different equilibrium distribution.

So I do not completely agree that the idea applies here.



I don't either, but it's fun to talk about. :)

The killing-your-great-grandfather remark I made seems specific to travelling back in time, yes... I should have stayed with more general examples because my idea isn't particular to time travel... This talk of mine of "parallel universes" was really just to gain a better conceptual model of making decisions in our own world, and to drive home the idea that different choices do not affect the ultimate outcome.

I don't think it works that well for a bunch of reasons but again, it's neat to discuss. If we were to get down and specifiy our populations (ie what exactly are we studying) and time intervals, the idea might hold.