Is that true every event has %99.99 chance to occur eventually if the time is infinite ?
Why did you pick 99.99 ? There is nothing special about that number.
Events which defy the laws of physics have a zero percent chance of happening regardless of the length of time but I believe the theory is that in an infinite amount of time, eveything that can happen will happen. I'm not convinced myself but that's personal prejudice, not based on science or math.
Well sorry I meant the event that are physically possible. Thanks for your comment.
There is a law that says "the worst is yet to come". It's in wikipedia also.
So that means if the tallest man on earth is 2.40 meters tall, if we wait long enough somebody 3 meters tall will turn up.
I have in fact tried this using random sample from the normal distribution and noted the extreme values. With 1000 samples it gives me an extremum of say 3 standard deviations. With 5000 a bit higher. With 15000 higher and so on. The extremum keeps on increasing.
I don't see what this has to do with the subject at hand, which is "if it can happen it will happen". Sure people will be shorter and taller than the norm and sometime to surprising degrees, but so what. There are NOT going to be 50 foot tall people.
A more interesting question, I think, is since it IS physically possible, will there ever be a person who has one Asian parent and one African parent, and is exactly 7' tall (give or take 1/16"), and has one leg just slightly shorter than the other, and has one brown eye and one blue eye, and who has blond hair, and who has 6 fingers on his left hand, and who has buck teeth and who was born with no ear lobes and a deformed left big toe.
The "everything that can happen will happen" thesis says yes there will. I'm no so sure.
And this is why the normal distribution is just an approximation (and a very good one). Of course we'll never see humans of 20 meters since that is physically impossible. http://www.dinosaurtheory.com/scaling.html Just because a result is theoretically possible doesn't mean that it is realistically possible. In using the normal distribution, we know very well that we won't see humans of 20 meters, but it would be awkward and computationally inconvenient to set an upper bound to the height of humans.
No, this is not true. You might be thinking of the infinite monkey theorem: http://en.wikipedia.org/wiki/Infinite_monkey_theorem But what you should keep in mind that this does not describe reality in general. It describes a very specific situation where some very specific conditions must be satisfied. If those conditions are not satisfied, then not every event will necessary occur.
For example, consider the 3D random walk. So you just take a spaceship and start flying in random directions. It can be shown that you will not visit every point even given infinite time. On the other hand, in 2D, you will visit every point in infinite time.
Whether an event occurs or not given infinite time is a difficult question. You should know more details before you can decide it.
Interesting! Is there a brief reason why there is a difference between 2D and 3D for this?
Unfortunately, I know no intuitive reason for it. I can prove it though, but it's not very enlightening. I hope somebody else can give an intuitive picture of why this is true.
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