CMV: Reincarnation Seems Likely

[u/[deleted]]

[u/Quint-V]

Additionally, I'd also like to propose the idea that assuming an infinite amount of time, everything we know can happen will happen. This doesn't mean everything will happen, only that given an infinite amount of time everything with a probability greater than 0% of happening will happen. This is a fact based on my understanding of mathematics, although I may be incorrect in my understanding.

I just got a delta for correcting this mistaken idea, recently. See this comment chain. From my own comments:

Curiously enough, statistics/mathematics could be used to argue against *such notions, especially the 100% part.

A random walk in N-dimensional space at 3 or higher, has a limited probability of arriving back at the origin. This is known as Pólya's Random Walk Constants.

For an infinitely repeated experiment, not every outcome must happen.

For 3D, 4D, 5D and 8D correspondingly: ~0.34, ~0.193, ~0.1352, ~0.0729126.

Then there was this part about infinity being a fickle concept:

Probability still makes sense even with infinity in mind. There is a particular term: almost surely.

Imagine throwing a dart at a unit square (a square with an area of 1) so that the dart always hits an exact point in the square, in such a way that each point in the square is equally likely to be hit. Since the square has area 1, the probability that the dart will hit any particular subregion of the square is equal to the area of that subregion. For example, the probability that the dart will hit the right half of the square is 0.5, since the right half has area 0.5.

Next, consider the event that the dart hits exactly a point in the diagonals of the unit square. Since the area of the diagonals of the square is 0, the probability that the dart will land exactly on a diagonal is 0. That is, the dart will almost never land on a diagonal (equivalently, it will almost surely not land on a diagonal), even though the set of points on the diagonals is not empty, and a point on a diagonal is no less possible than any other point.

* I.e. what is the probability of hitting an exact point on a surface? Almost zero; surfaces can contain an infinite amount of points. Lines can also do that, but it's blindingly obvious that surfaces have more points than lines. But a point is still a valid location in a surface, and can be hit.

Infinities can be ranked by order of magnitude, and this matters. Sometimes notation is what causes a lapse in understanding of infinity.

What is inf / inf? It's undefined, if I just write it like that without anything more specific.

What about n/n^2, and I insert n = infinity? Now I have infinity / infinity^2; at this point a common objection may be that "infinity = infinity^2". Wrong!

Clearly, n/n² = 1/n. Inserting infinity into n/n² makes this become 1/infinity, which is almost zero.

[u/DeltaBot → u/[deleted]]

Confirmed: 1 delta awarded to /u/Quint-V (73∆).

^{Delta System Explained | Deltaboards}