[Karl_Lembke]

How do you quantify similarity of shape and structure?

I don't think they meant to quantify those attributes, rather I thought they meant the sequence of the proteins local to the active parts of the structure, the bonding sites for instance. At those critical points the sequence would be more sensitive to change and likely to be selected out/in.

I suspect you're right. But your original question was,

Why provide a number when it shows a difference and only a vague "much more" when the similarity is purported to be important?

The point is, it's very easy to quantify amino acid substitutions, and the differences and similarities involved. It's considerably less easy to quantify differences in shape and configuration.

For example, how would you handle the task of rating clouds to see whether they look more like Thomas Jefferson or Madonna? How would you assign a numerical value?

[Black Agnes]

There are also companies that sell various programs that indeedy do asign a 'number'.

Proceryon BioSciences

Each method/program has its own scoring criteria but they will tell you if a particular sequence might possibly assume a given shape. Also, they allow you to compare various protein backbone shapes (from previously determinec X-TAL structures) to find an RMS for one vs. the other.

[AndrewC]

For example, how would you handle the task of rating clouds to see whether they look more like Thomas Jefferson or Madonna?

The simplest would be a 2D ratio of the area covered by the purported image to a circle circumscribed about a central point determined by the midpoint of the long axis of the image in the cloud. This ratio would be compared to a like ratio determined for the image of each (in)famous persona. The closest match determining the Madonna-esness or Jefferson-esness of the cloud image. (you actually are stating the problem as it relates to the proposed automatic airport identity software. The problem is definitely solvable)