That's very interesting, thanks. (I hadn't actually expected to have informative replies to this post; I'd expected a slew of individual votes for wildly differing orders which would further increase my incomprehension!)

The ordering of elements, on the other hand, I'm now further bemused by. I had it firmly fixed in my head that the canonical order of the four elements was Earth, Air, Fire, Water, and I know that NetHack at least agrees with me :-) On the possibly shaky assumption that somebody might at some point have done some research while writing the endgame sequence in NetHack, do you know if there's a reason for the EAFW ordering?

Yep. That's the calling order used in left-hand-path or Black magic, actually.

My best guess at the reasoning behind this (though other occultists might tell you something different) is as follows. East is the source of light, since that's where the sun rises, so right-hand-path rituals start with the East. North has an association with evil (for a range of possible reasons) - among other things, if you look at a really old graveyard you'll find no graves on the North side except those of suicides and the unbaptised - and so for left-hand-path magic, you start there.

You're right, though, that those without occult training usually tend to list EAFW as the default order. I have no idea why this came about. Strange, now you mention it...

Fantastic, thanks! Truly you are a mine of information.

(My layman's understanding is slightly surprised that the left-hand path doesn't then go widdershins after starting with north, but I'm sure this is because "do everything widdershins if you have the choice" is a massive oversimplification of the black magic ethos :-)

The problem is that the subject of ceremonial magic is such a sprawlingly complex one that it's very hard to determine accurately who did what and how you should do it in future. If you go back to the older grimoires, even the most egregiously self-aggrandising rituals are backed up with appeals to God and the Archangels and use the right-hand-path formulae. Nobody generally likes to put their hand up and go "I'm evil, me!" especially not in an era where the rack and the stake awaited you if you got done for it; so doctrine on Black Magic practice is skimpy and messy to say the least. Meanwhile, most modern grimoires draw heavily on the author's imagination rather than on the older texts. It's damnably hard to piece together a logical, unbroken chain of development for ceremonial magic, so the rule these days tends to be "do it how you think it should be done."

So in summary, yes, you can go widdershins if you want to, but not everyone would. :)

My impression from modern "white" texts is that the direction of rotation affects the accumulation of power indiscriminately.

I suspect you may wish to blame Earth, Wind & Fire (http://www.earthwindandfire.com/). That's definitely where I'd have got it from, via my mum's record collection.