It may look a little like one of those discussions about "which  viewpoint is right."  But that's the opposite—in an important sense—of what it’s really about. 

Let's take a step or two across an edge or two of easy human comprehension...

“Is that right?”

Validity of information is important.  (Information is central to living organisms; in many diverse ways.)  And many discussions become full of sound and fury over that important question.  And then go no further.

“Is that sufficient?”

Sufficiency is the next step.  And the next, and the next, and . . .   Sufficiency is at least as  important as validity.  Adequacy, sufficiency, completeness, scope, and wholeness are all too frequently "unseen" criteria, hidden from thought while hot debate boils over "validity." 

But validity is only one criterion for ideas, for opinions. for analyses.  There are many more.

Dimensionality is an abstraction that unites a lot of those “sufficiency” things that get persistently missed.  Now, this isn’t the “higher dimensions” of a sci-fi movie, where the heroes do superman things by jumping into “wormholes in the eleventh dimension.” 

This dimensionality is much simpler.  And very much more abstract—and, therefore, very much more subtle.  That's why it goes unseen so often, so persistently.

This is the dimensionality of color vision, which is the key concept that distinguishes  between a colorblind human and a “color normal” human, and between either and the color vision of a bird.  It’s the dimensionality of the “four-space” of relativity, of the “degrees of freedom” of thermodynamics, and of the "rank" and "order" of a tensor.  It’s one of the demons in the details of college physics and math that destroys grade point averages of humanities majors who dare dip into the “hard sciences.”  It may mystify even physics and math majors until they get a little worldly experience…and sometimes it just keeps right on mystifying. 
 
 

Furthermore, dimensionality is about parameters, the many different factors that intertwine, interact, interfere with our wish for simplicity, and mystify us until we discover some new way of looking past our pinched vision.  Vision so pinched that we might see no distinction between "parameter" and "perimeter."

When Jean Piaget asked the question, "What are the most sophisticated information insights that we humans develop as we mature?" he found a bunch of information processing skills that let us see the subtleties of multiple parameters.  These mental developments, which he called "formal operations," lead to recognizing multiple parameters, identifying the relevant from the irrelevant, eliminating "subtle" contradictions (they don't seem very subtle if you see them), systematically imagining alternatives, and a bunch of more technical things that lead to understanding of ratios and proportions and being able to extrapolate to unattainable limits.

This is, of course, the perception of modern science and mathematics.  It is the insight into the abstract that goes pervasively and persistently missed—making a lot of ideas pre-scientific (in strikingly predictable ways) and preposterous (when you "see" the science).  This vacuum of failure to abstract is the breeding ground of pseudoscience.

Pseudoscience still rules the thinking in our culture.  In the press, on TV, and even, somewhat, in our schools.  The science is simple, but it remains very subtle.  We try, on this Knowledge for Use Web site, not simply to declare, or point to, what is pseudoscience, we try to demonstrate it.

The decision to build Glen Canyon dam was not an invalid decision.  BuRec is extremely competent in analysis of many of the parameters of water use, and of the tensor analysis needed to build strong structures.  But validity was only a first step toward a decision, and then the Bureau stopped taking steps. 

The accompanying political processes stumbled at every step over unseen dimensions. 

Let us learn to look where we are going.  Let us learn to see beyond the merely "obvious."  Let us learn not to go around scribbling our graffiti on Mother Nature's most beautiful and sacred walls.  Let us understand  what's wrong with taking pride in our vandalism.