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-1 Why are there different usages of the articles with 'mind' throughout the entire article. It seems to me that this is done in arbitrary way? The mind is a set of cognitive faculties... ...what constitutes a mind and what are its distinguishing properties. ...or whether mind can also be a property of some types of human-made machines Some see mind as a property exclusive to humans whereas others ascribe... Please, explain meaning of the use of a, the and zero article with 'mind' in here: https://en.wikipedia.org/wiki/Mind articles share | improve this question edited 2 days ago ...

8 2 I've read on a paper that, in the two dimensional case, if you start from the origin and take steps of length one in arbitrary directions (uniformely on the unit sphere $S^1$ , not left-right-up-down), the expected distance after $n$ steps from the starting point is approximated by $sqrt{npi}/2$ (source: https://pdfs.semanticscholar.org/6685/1166d588821456477f2007a37bf0428a2cf2.pdf). I was wondering if there was a similar formula for higher dimensional random walks, which means: Starting from the origin in $mathbb{R}^d$ if I take $n$ steps in random directions (which doesn't have to be aligned to any axes, can be any uniformly chosen random direction taken from the sphere $S^{d-1}$ ), what is the expected value of the distance where I end up from the origin? e.g. how distant is the point from ...