depends on what is meant by "size."  The basketball coach wants height; the football coach wants weight  (actually he wants mass, and the distinction is important to anyone who understands Newton's discoveries of three centuries ago–and which touched off the "scientific revolutions" we have today).  There are many different aspects to "size."  When we do the usual ranking (linear) we are confusing those different aspects.  We usually don't know we are confusing them.  We think–we feel–that unique rank order is the meaning of measure, the meaning of putting things into mathematical language.

It's a little hard to see where this should lead, so we use color as an alternative exemplar.
 

Here the shades of blue might indicate "intelligence."  Most people think of intelligence as capacity (but sometimes speed) of memory and recall.  Math prof Jerry Manheim sees the oversimplification of this viewpoint when he says, "A measure of how good one is in math is not what one can remember but what one can afford to forget."

Learning, memory, recall, and even linguistic fluency, are important, but in science and math there's something else that's far more important.  It's a bunch of...
   
?  What should we call this important aspect of intellect?  "Insight"?  "Seeing"?  "Formal operations" (Piaget's slant)? "Exemplars"?  "Magic" (Feynman's forte)?

It definitely isn't the rote and ritual that the vast majority of science students see science as being.  It's a set of intelligence components that are orthogonal to that simpleminded notion of "g factor" and which is exemplarized by our comparison of two different physics faculty (from two different universities) in our intriguing observations of Post Modernism. 

We're taking only a first step when we replace those blue dots that represent g-factor of intelligence with dots having a second component of color.  J. P. Guilford finds, with his factor analysis (one 19th century development of the math of multiple components), seventeen different orthogonal components within what we call "intelligence."

If you take a magnified look at the tiny color-CRT dots on the screen of your computer monitor, you will see that those "BI-CHROMATIC" circles (in the middle of the column to the right) have the blue CRT-dots turned off.  Only the red and green dots are in use.  They are the two dimensions of the ordering.  Two "degrees of freedom."  Two "components" of a vector measure.  Two of something that is almost universally seen as always one.  By psychologists looking at human intelligence.  By economists looking at value, benefit, cost...  By bigots looking at superficial qualities of "other" people.  By "authoritarian personalities" looking at social structures, such as in the miltary, in prisons, in corporations, in families, in neighborhoods...

Scalar measure is rare in the real world.  Very, very rare!  Oversimplification is the rule.