Can the impossible happen in an infinite universe?

Pulse Fart

Given n opportunities, the chance of an event with probability of 1/n happening is p = 1 - (1 - 1/n)^(n-1).

For example, the chance of rolling a 6 given six rolls of the die is:

p = 1 - (5/6)^5 ≈ 60%

None too complicated.

It becomes interesting if we let n tend to infinity, ie consider infinitely many opportunities for infinitely unlikely event to happen. The probability p tends to 1 - 1/e or ~63%, suggesting that, given infinitely opportunities, an impossible event is more likely to happen than not. :pac:

Joe1919

Your argument has similaraties to the eternal recurrence argument i.e. Given that Time is infinate and matter ( and its combinations) is finate relative to time, the probability exists that the exact same combinations of matter will exist some time in the future and hence, we will all return........(or something like that).
http://en.wikipedia.org/wiki/Eternal_return

me_right_one

Hmmmm.....

A) Nothing is impossible
That doesnt guarantee that every possible event will actually occur

Hence...

C) Everything is possible, including the possibility that every possibility will, or will not, occur

skelliser

define whats possible and impossible in the context that they are human constructs

orestes

skelliser wrote: »

define whats possible and impossible in the context that they are human constructs

Some things are be their very nature essential and unalterable, therefore some things are inherently impossible. It is impossible for the radius of a circle to be exactly one third the length of the circumfrence same circle for example.

me_right_one

orestes wrote: »

Some things are be their very nature essential and unalterable, therefore some things are inherently impossible. It is impossible for the radius of a circle to be exactly one third the length of the circumfrence same circle for example.

We're talking about an infinite Universe here, not just what we're used to on Earth. If you had a circle and draped it over the event horizon of a black hole for example, the frame dragging effect would make it completely and utterly possible for the radius of a circle to be exactly one third the length of the circumfrence same circle.

Black Swan

If the universe is indeed infinite, there may be infinite answers to your question?

Joycey

orestes wrote: »

Some things are be their very nature essential and unalterable, therefore some things are inherently impossible. It is impossible for the radius of a circle to be exactly one third the length of the circumfrence same circle for example.

A circle is a human construct. Our concept of circle does not rely on there being any instance of a perfect circle, where what you said above would apply, in existence. When you say its impossible for the radius of the circle to be exactly one third... , you are saying that if such a figure were to exist, it would not match our concept of circle. It has nothing to do with there being some 'objective' state of matter which is 'impossible'.

waitinforatrain

Pulse Fart wrote: »

Given n opportunities, the chance of an event with probability of 1/n happening is p = 1 - (1 - 1/n)^(n-1).

For example, the chance of rolling a 6 given six rolls of the die is:

p = 1 - (5/6)^5 ≈ 60%

None too complicated.

It becomes interesting if we let n tend to infinity, ie consider infinitely many opportunities for infinitely unlikely event to happen. The probability p tends to 1 - 1/e or ~63%, suggesting that, given infinitely opportunities, an impossible event is more likely to happen than not. :pac:

What if n is infinite?

(or worse, zero )

edit: Something's off with either your formula or your example. 5/6?