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.
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.