What three variables is the tag cloud conveying by its tag sizes, and the tags' x and y locations?

The x-y of the tags is pretty much irrelevant -- I don't know if anybody's actually trying to use that to convey anything.

The tag sizes are pretty unambiguous though, which is where the clouds do better than ordered lists. Ordered lists are inconsistent: sometimes they're ordered alphabetically, sometimes they're ordered by importance, sometimes by popularity, sometimes they're not ordered at all, which is visually identical to an ordered list.

A tag cloud on the other hand always relates the tag size to the number of items with that particular tag. That's the visual distinction that makes them more useful than a simple list.

but a simpler way to add this information is to title the list. "Tags by popularity". You don't have to go to the trouble of inventing a whole other representation. I'd contend that adding a little bit of information to the title is much better than going to a tag cloud. The visual cue from the tag cloud (that the bigger things are more important) is inherent in the ordered list too (the things at the top are more important).

> sometimes they're not ordered at all, which is visually identical to an ordered list. An ordered list is always ordered, the only question is whether ascending or descending. And a tag cloud where the terms are randomly sized is visually identical to a tag cloud where the size means popularity...

I think the benefit of tag clouds is purely aesthetic. They just look prettier in certain places, and even that point is debatable.

You could have a list in decreasing order of importance/fontsize... I think it's harmful to use a seemingly 2D representation when the spatial relations are meaningless. 1D (a list) would be enough.

But then you lose alphabetical order.

Like any other text that word-wraps, x and y are not separate axes. The two axes it does display are "frequency" (size) and "lexical order" (position). An ordered list can only display one of these.