Zizek often draws on Lacan term the Big Other; what is this and what does it mean?
One supposes that there may also then be a little other - is this right?
What would be sensible examples of either kind?
Well, the examples you offer seem to be oppositions...East v. West, a discourse that valorizes belief v. a discourse that valorizes knowledge, and man v. woman. The “Big Other” is the symbolic texture of human subjectivity, whence come norms, expectations, desires, prohibitions, regimes of representation, guaranties of meaning, and many other things.
The "Other" in Big Other can be distracting; it tends to personify, if not caricature, what I described in the previous sentence. I think that many people tend to think of the Big Other as a Big (br)Other, which is a mistake. The Big Other is purely virtual, and of it Lacan would often say that it doesn’t exist (he would also say “there is no Other of the Other,” which was a way of saying that there is no metalanguage that could provide a guarantee to our meanings).
Regarding the relation between man and woman, it is reasonable to see them as being little others for each other; in some ways this is accurate, but I think only in a superficial way. The relation between little others is, one some level, always one of narcissism, aggression, and competition. If you think about it, to some extent, this pertains to all relations between all individuals.
But the relation between ‘man’ and ‘woman,’ this is something a little different... I think that lacanians would tend to speak of one as being the symptom of the other, and I think the same is true for the relation between Orient and Occident. As to the relation between Religion and Philosophy, I don’t know.
Since little others can be thought of as neighbors, fellow citizens, enemies, friends, peers, or lovers, and Big Others can be thought of as collections of social conventions, codes, norms, laws, etc., why shouldn't we simply abandon the lacanian parlance and call little others 'persons' and Big Others 'cultures'? What is it that makes the other "other"?
What is it that grounds the Other's (or other's) alterity, that makes it fundamentally unassimilable?
Here is a link to an article by J.A. Miller that addresses this idea.
this wiki site is a good Lacan resource, at least - I have encountered it a few times.
The big Other designates radical alterity, an otherness which transcends the illusory otherness of the imaginary because it cannot be assimilated through identification. Lacan equates the big Other with language and the law, and hence the big Other is inscribed in the symbolic order.
So the little other
is inscribed in the imaginary order as both the counterpart and the specular image.
The imaginary is the realm of image and imagination, deception and lure
and so the other is what we imagine other people to be, whereas the Other is their symbolic existence - which is the Otherness that operates within the law.
The law is
the set of universal principles which make social existence possible
and so, the Other is the Other that we interact and are obliged to, etc..
It may help, if this just seems like STUFF, to read an article or two of Lacan's and see how he uses these concepts. E.g. in the purloined letter.
The first is a glance that sees nothing: the King and the police. The second, a glance which sees that the first sees nothing and deludes itself as to the secrecy of what it hides: the Queen, then the Minister. The third sees that the first two glances leave what should be hidden exposed to whoever would seize it: the Minister, and finally Dupin.
I read the first glance to be the imaginary, the second glance the symbolic, and the third the real. But it was quite some time ago and I should add the caveat that I have been told I was wrong there, by a fan of Zzizek.
The Big Other is simply the symbolic order as it exists for an individual subject (language, law, culture, etc.)
And yes, there is a little other as well. The little others are essentially other individuals.
Lacan writes them "Other" and "other" (Autre/autre in french).