[kgwgk]

Sure.

The point is that you wrote that « you can pick any point […] » and when toth pointed out that « there is always a choice of origin implicit in some way » you replied that « you could use an uninformed improper prior. »

However, it seems that we agree that you cannot pick a point using an uninformed improper prior - and in any method for picking a point there will be an implicit departure from that (improper) uniform distribution.

[rssoconnor]

Oh.

When I said "you can pick any point P", I meant universal quantification, i.e "for all points P", rather than a randomly chosen P.

I did say "choose P", which was pretty bad phrasing on my part.