The Limits Of Probability

We were talking about infinity in another thread a few hours ago and it inspired me to watch a really cool documentary about infinity: To Infinity and Beyond.

This really got me thinking about just how far the limits of probability stretch. For instance... if our Universe is Infinite, which it seems to be, then it's a mathematical certainty that somewhere out there is a planet exactly like Earth. And a person exactly like you. In fact there would be an infinite number of copies of you out there. There would even be copies of our Universe out there.

Well maybe the Universe isn't infinite you say? Well think about this... is there an end to time? What will happen if there is no end to time? That's right... an infinite amount of things will happen throughout that infinite amount of time. And when you have an infinite amount of time or space for things to happen, everything and anything possible WILL eventually happen.

A monkey will type out the entire works of Shakespeare? It will happen. The same person will win the lottery ten thousand times in a row? It'll happen. A planet will be ruled by intelligent Unicorn creatures? It'll happen. All these things will eventually happen at some point... anything within the laws of physics is bound to happen eventually, no matter how small the chance might be, it's still a chance which will eventually manifest.

Furthermore we can never know when these anomalies could occur. A major statistical anomaly could occur at any moment. What does this say about the logic of gambling? Can a person really have ten thousand wins in a row? Would a monkey ever really randomly type out the entire works of Shakespeare? I mean it's physically possible for a monkey to do it, but would it really happen... has it already happened.

This is a some what disturbing subject honestly... it really pushed my limits of what is actually possible. I know deep inside me that infinity is real... or else I wouldn't even be here right now. Time does not simply end forever (it may oscillate on and off though), and the chances are space doesn't simply end either. And so the prospect I am presenting here is frighteningly real my friends. I welcome your thoughts and responses on this mind-boggling subject.

OMG I just had the funniest thought... for those of you who believe you'll have an eternal life in Heaven. Just imagine all the "major statistical anomalies" which will occur in that time!

Originally posted by ChaoticOrder

This really got me thinking about just how far the limits of probability stretch. For instance... if our Universe is Infinite, which it seems to be, then it's a mathematical certainty that somewhere out there is a planet exactly like Earth. And a person exactly like you. In fact there would be an infinite number of copies of you out there. There would even be copies of our Universe out there.

It would not be a certainty but almost surely to be the case.

reply to post by john_bmth

While there is no difference between almost surely and surely (that is, entirely certain to happen) in many basic probability experiments, the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces.

The difference between an event being almost sure and sure is the same as the subtle difference between something happening with probability 1 and happening always.

If an event is sure, then it will always happen, and no outcome not in this event can possibly occur. If an event is almost sure, then outcomes not in this event are theoretically possible; however, the probability of such an outcome occurring is smaller than any fixed positive probability, and therefore must be 0. Thus, one cannot definitively say that these outcomes will never occur, but can for most purposes assume this to be true.

Pretty weird stuff... can you explain in simple terms how that is relevant to what I said?

reply to post by ChaoticOrder


When the probability is 100%, it is as close to certainty you can get without reaching it, which still makes it an uncertainty. The Infinite Monkeys theorem colloquially states that an infinite amount of monkeys hammering on typewriters, one of them will type out the complete works of Shakespeare but this is not a certainty, but almost a certainty. At least, this is how my mathematician friend explained it to me So with your infinite universe, the chances of an Earth clone existing is almost surely, but not a certainty. It's a minor point but one that slightly alters one's view of the infinite.

reply to post by john_bmth


Ok... interesting point. So even though it's almost certain a copy of me exists out there some where, it's not absolutely certain? But it doesn't seem that simple to me... in an infinite Universe there should be an infinite number of copies of me out there. With infinite time there should be an infinite number of copies of me occurring over and over again. I don't see how the mathematics could possibly say it isn't certain when given an infinite amount of time or space, common sense would tell me it is inevitable. But then again common sense doesn't always work in these abstract situations. And that's exactly why I'm asking just how for the limits of probability can go.

reply to post by ChaoticOrder


Because probability is not certainty. I could roll a dice 1,000,000,000,000 times and although i will almost surely get a 6, it's not a certainty. Likewise, If I keep rolling an infinite amount of times I will almost surely get a 6 but again, it's still not a certainty. For all intents and purposes we can say I will roll a 6 but you can only say with certainty once the event has transpired, i.e. in retrospect.

reply to post by john_bmth


Yeah I can sort of understand the logic of it now... I mean what is to stop you from getting a 6 an infinite number of times? That's a possibility... a trippy possibility. Mind now melting...

reply to post by ChaoticOrder

Yeah, that's why it's a pickle for the mind My brain hurts

Equations that sum to infinity usually are good enough after a few terms.
Even integrals to infinity just mean a transformation of variables.

Christopher "Kit" Marlowe wrote Shakespeare in a spy network so his
life would be spared by the Queen. How many plays are in Italy where
Kit was hiding and often at England's Embassy. Kit died of bad wine
long after Shakespeare and wrote the epitaph under the 'Bards' statue.

Just as good a story or conspiracy as monkeys doing anything.
Things do not happen by probability they happen by environmental energy.
A store owner said not to get involved with UFOs as I went to buy a magazine.
Did they know the disreputable type that put them up for the store to sell.
Same with the so called probability masters from Einstein or Heisenberg.
The knowledge they did find the Illuminati prevents them from telling us
and must belabor the small talk.

reply to post by TeslaandLyne


I'm not sure I understood a single thing you said but it sounds interesting.

Originally posted by john_bmth
reply to post by ChaoticOrder

 

Yeah, that's why it's a pickle for the mind

My brain hurts

edit on 2-10-2012 by john_bmth because: (no reason given)

So many of the things I would like answers to make my brain hurt. I'm not a genius my IQ is 133, which is ok, but I can't wrap my head around most of this quantum physics, infinite universe stuff. I need a pill to jack the IQ up to around 200 I guess.

Originally posted by ChaoticOrder
reply to post by TeslaandLyne

 

I'm not sure I understood a single thing you said but it sounds interesting.

It wasn't easy seeing your post but only took out anything I could scour because
I did not want to jump into any thing like Alice in Wonderland and get mind trapped.

Like common text book science we have heard the monkey story from these people
and its like an arcade attract to get you interested and all there is left is to keep on
with where they ended up. A professorship or locked in a conspiracy.
ED: Well I posted thee things. They must relate.
My paragraph one. Math equations with infinity.
Probability has math and infinity.
You mentioned Shakespeare so I mentioned the latest update from conspiracy
seekers or those opposed to the 'official' word.
And I topped it off with my bad opinion of the world of probability talkers.

Originally posted by ChaoticOrder
reply to post by john_bmth

 

Ok... interesting point. So even though it's almost certain a copy of me exists out there some where, it's not absolutely certain? But it doesn't seem that simple to me... in an infinite Universe there should be an infinite number of copies of me out there. With infinite time there should be an infinite number of copies of me occurring over and over again. I don't see how the mathematics could possibly say it isn't certain when given an infinite amount of time or space, common sense would tell me it is inevitable. But then again common sense doesn't always work in these abstract situations. And that's exactly why I'm asking just how for the limits of probability can go.

its not certain or almost certain or rational to think there is a copy of you that exists out there,.,.,..,

what does that even mean?

you hardly exist compared to objective reality.,,.,.,.

everything that exists within the universe is the universe,,, you are a copy of it,,, always,,,

all things that exist are an expression of the possibilities of the components of the universe interacting,,,

what im trying to say is,,.,.,.., if an entity existed on another planet,,,, made of the same exact stuff as you,, looked just like you,,, was born by the same seeming parents,.,.,.,. then it will still have very little to do with you,,,,, just as you have very little to do with you..,,..,

if you see a squirrel in your backyard,,,, then one in china,,,,,, do you compare them as copies? what about stars in the universe,.,.,.,. is there a star thats a "copy" of ours?

reply to post by ImaFungi


Obviously you are correct. There would be no magical connection between me and any of my "copies". But I don't see how that's even relevant really... the point it's weird to think a being "almost surely" exists out there exactly like me. But beyond that it's the math and probabilities which are of real interest here, not the philosophical or metaphysical implications.

Originally posted by ChaoticOrder
reply to post by ImaFungi

 

Obviously you are correct. There would be no magical connection between me and any of my "copies". But I don't see how that's even relevant really... the point it's weird to think a being "almost surely" exists out there exactly like me. But beyond that it's the math and probabilities which are of real interest here, not the philosophical or metaphysical implications.

If we follow your train of "conjecture" even further down the rabbit hole, we have to assume that amongst the "infinity of infinities" out there, your double DOES exist right down to the very last quantum match. This means that one or more of your "doppelgangers" is feeling, experiencing, thinking, hoping, wishing, etc, etc IDENTICALLY to you for every one of the seconds that you both experience and live through.
NO differences at all down to the quantum level.

So my question to you ... which one of you (you and the mutitude "other" you's) can claim to be the original one ?

reply to post by tauristercus

So my question to you ... which one of you (you and the mutitude "other" you's) can claim to be the original one?

I think the point is that there is no original one. Which H20 molecule in a glass of water is the original one?

Originally posted by ChaoticOrder
reply to post by ImaFungi

 

Obviously you are correct. There would be no magical connection between me and any of my "copies". But I don't see how that's even relevant really... the point it's weird to think a being "almost surely" exists out there exactly like me. But beyond that it's the math and probabilities which are of real interest here, not the philosophical or metaphysical implications.

ok,,, now also....

the universe might not be infinite in the way you imagine.,,..

the universe comes into existence.......
man comes into existence......
man creates and comprehends his created concept of infinity....
you ( part of man) now thinks that some aspects of this concept of infinity.. equals the universe,, in very abstract ways,,
what if the universe was more like physical pi....... with no repeats...

reply to post by ImaFungi

what if the universe was more like physical pi....... with no repeats...

That's sort of the same concept we reached earlier when we were talking about the dice. My basic assumption was that everything possible will eventually happen in infinity, if you travel far enough or wait long enough... but what about the possibility that the same thing will repeat over and over again? That's a possibility... yet it eliminates all other possibilities. Another weird but valid possibility is that nothing the same will ever occur throughout infinity (what you just said). But if we are to assume everything possible must happen... how can those contradictory possibilities happen simultaneously? Clearly there is a deeper meaning to all this lurking around here...

Ok you beat me...

How do you link "Infinity" with "Probabillity"

I dont get it....