Why is lexicographical organization not considered a continuum?

Question

http://usabilityfriction.com/2009/09/29/five-hat-racks/

Both Lexicographical (alphabetical) and Chronological seem like they are members of Continuum to me. They can be plotted like any other member of Continuum along an axis, and are infinite. If Continuum is really just shared measure, then Chronological and Lexicographical definitely qualify. However every source I see indicates that from a design perspective:

 { x | x ∈ Chronological   } ∉ Continuum 
 { x | x ∈ Lexicographical } ∉ Continuum

Why is this the case?

Answer 1

First of all, they could be perceived as subsets or specific cases of a continuum, common enough to get special treatment.

But there are also differences.

Alphabetical order is "arbitrary" to some extent, it doesn't tell you anything about the actual properties of an item. If you deal in clothing and your continuum is Size, you could say "I want to see the clothing for sizes M-L-XL". Saying "I want to list the people beginning with letters C-D-E" is meaningless, there will be no other characteristics shared by people whose names begin with C. The fact that an alphabet has a standard order is very convenient and lets us introduce some order into lists of people etc., but it's still completely arbitrary and not too useful.

And that's without getting into the issue of different languages, where you could have a completely different order for the same items. This is not the same for continuum - no matter what units you use for Weight, the order would be the same.

To use the original article's words, Continuum is grouping by magnitude. Alphabetical lists don't really have a magnitude, just a conventional order.

Regarding chronological order - I think that it may or may not be the same as Continuum, depending on the items and what the chronology refers to.