Do you have a dumb question that you're kind of embarrassed to ask in the main thread? Is there something you're just not sure about?
This is your opportunity to ask questions. No question too simple or too silly.
Culture war topics are accepted, and proposals for a better intro post are appreciated.
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Notes -
A simple example:
A random walk in 1D and 2D space is recurrent, and the odds of returning to the origin over an infinite amount of time approaches 1.
On the other hand, a random walk in 3D space converges to a finite, <1 value. The space of possible outcomes expands faster than you can explore it.
"A drunk man will find his way home, but a drunk bird may get lost forever."
I don't, however, think this is a rebuttal of a Boltzmann Brain. For any given volume of space-time, there is a finite set of distinct structures it can take, and over an infinite amount of time, the odds of instantiating one approaches 1. The key difference here is that we are concerned with finite volumes with a finite number of potential arrangements over infinite time, as opposed to an infinite volume in the case of random walks in three dimensions.
( @faul_sname , if you're still around, care to comment?)
An unbiased random walk (where each direction is equally likely) in 1D and 2D space is recurrent.
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