Ignorance and Stable Conceptual Structures

When we say "I trust this expert's opinion on this topic because he knows more than I do." we are doing something amazing, or at least it's amazing when that opinion goes against our own.  We are exercising a skepticism about our own reliability.

Our beliefs about the world tend not to change.  We think our current view is about as correct as anything out there.  Since reality is filled with an infinite set of unknowns, the areas of our own ignorance about which we are actually aware, is quite a small sliver.  Combined with the fact that our brains can only inhabit one interpretation at a time, its vital that we maintain this uncertainty. Let's look at a simple, concrete example of this limitation.

Is this painting a collection of birds? A portrait? Is it REALLY both?  Perhaps it is best understood as a demonstration of artistic ambiguity, or none of these, most fully appreciated by a framework still unknown?  

Unless we stumble across clues that get our attention, it's all-but impossible for us to have any awareness of our own limitations and biases, even in science: our most reliable method of investigation.  With this painting seen from a distance, it makes perfect sense as a portrait and we might have no reason to look further...but more importantly: if we don't like birds, we have an incentive to discount bird interpretations. This incentive is directly proportional to our emotional investment.

Debates on the evolution of stellar clusters and super clusters were completely unknown to me prior to a conversation with my dentist who participates in them. Such arguments had been raging over various theories and models for years, and while it is impossible for me to have an opinion about arguments about which I'm ignorant, what nagged me most is that I never even suspected such debates were taking place...despite having a more than passing interest in the evolution of the universe, at least insofar as it relates to cosmology.

Within areas of debate we understand, however, there are principles that identify stable conceptual structures, as identified in book that should be required reading at the National Science Foundation and its Board.

One principle is that stable concepts do not have categories which overlap.  Everyday communications which are clear demonstrate this. When sodium and potassium chloride were both on the breakfast table one morning, my wife did not offer overlapping "salt". Instead, she asked: "Sodium?" to which I distractedly answered: "Nah."

"Potassium?"  "K..." after which we burst into laughter. 

The second principle is "exhaustion".  Stable concepts possess categories that exhaust all expected possibilities.  The model of chemical elements in the periodic table demonstrates this, as we do not expect to see any new chemical elements between hydrogen and uranium, but minor violations of this principle are allowed which do not threaten the structure, however.  Such as when a new isotope or ionic form of an element is found.  These can even serve to reinforce the perceived strength of the conceptual structure by demonstrating its ability to accommodate new discoveries.

The final principle is "inclusion", which is akin to class inheritance.  All atoms possess attributes of an element: atomic number, mass, and a nucleus/electron orbital structure.

When serious violations arise that cannot be accommodated by minor additions to the hierarchy, revolutions occur which transform the scientific landscape.  New areas of research are opened and the mistaken assumptions of the past are exposed.  

Upcoming posts will focus on this change - and the problems and risks resulting from widespread misconceptions and even greater ignorance about this topic.  Structuring this analysis will be the just-release high-level report from the National Science Board, responsible for studying and recommending policies to support "transformative research" as an explicitly stated strategic goal.