> The whole concept of a permeable membrane, i.e. essentially stuff that has holes but still is "one piece" (something like a sieve or strainer or colander or net or anyhing of the kind), is something that IMHO requires 3+ dimensions. In two dimensions if a membrane has two or more holes then it's not a single membrane anymore.

By what reasoning would it not be a single membrane in two dimensions, but it would be in three dimensions? As far as I can tell your only support/reasoning is found when you write "IMHO"...