His neighbor, Mary, looked at the new paint job and knew that something was wrong.  She asked the proud painter,  "How come the two-tone paint job?"

The color cube diagram below shows how the two kinds of color vision see the colors.  The colorblind person can come to understand the difference between the different ways he and his neighbor see color, but only if he delves into the depths of abstraction of the mathematics and science of color vision. 

A person who has looked and seen can easily tell when someone else hasn't seen.   While, "Everyone's entitled to their opinion," some opinions surround a person with an aura of ignorance that is obvious to the person who has seen.  The insight needed to solve Martin Gardner's puzzle isn't very deep, and most people will be able to improve their aura through their discovery of the solution:

What is the direction, up or down, of the acceleration of a freely bouncing ball at the bottommost point of its bounce, that is, at the instant its velocity changes from down to up?

Most physics students first learn a lot about physics and quite a bit about acceleration.  They learn a lot of textbook questions and a lot of answers to those questions.  Then, when they encounter a situation where some understanding of physics would be a real advantage to them...their learning turns out to be useless.  They simply had not understood what they learned.

The answer to the bouncing ball question is utterly trivial when we understand acceleration—the answer is actually given in the statement of the question!  (Like in "Who wrote Bethoven's Fifth Symphony?")  Here lies the reason for the slogan "Learning is not our goal, seeing is."  It's also illustrates the often-unseen logic that rejects "teaching to the test."

Nevertheless, a remarkably high percentage of graduates of first-year college physics courses give wrong answers to questions like this one, questions that probe understanding, making it obvious, to those who "see," that they don't see.  The simplest questions about physics are often the most difficult.

Some people will sense a kind of glittering, bright and sharply defined aura surrounding the speaker, an aura of absurdity.  These people can probably articulate the errors; give them names, identify ways to correct them, suggest other errors that are related and will probably be made by the same people.  Many others will see the aura, but it's a little dim, and it's not quite clear precisely what the error is.  To some, the aura isn't seen at all, and the law sounds reasonable enough.  To more than we might wish, the aura seen is an aura of astuteness and reason, of leadership and resolve: "What a great idea!"
 
 

 "Might be..."?  We need "is"!  At the very least, we want to see valid evidence, and evidence that meets the kind of requirements that empowers science to overcome mistakes of observation and logic, to expand observation and thinking into aspects and dimensions that often get overlooked, and to avoid self-deception,--and perhaps deception by others who want to mislead us. 

"Might be... " without evidence is a red flag that warns us that the Prove Anything Ploy (PAP)is probably being applied.  "Prove Anything" starts with the conclusion, and then seeks corroborations and rejects disconfirmations.  In a world much simpler than the real one, finding a bit of corroboration might be all we would need, but in the real world we must sort through and evaluate complex networks of causes and effects, intricate alternatives of possibilities, and powerful wishes fed by robust human imagination. 

That oversimplified world is the world of pseudoscience: astrology, remote viewing, telekinesis, precognition, magical pyramids, spoon-bending by mental effort, alien abduction, biorhythms,...  We should add other unsubstantiated beliefs, too: belief that the lottery is a reasonable route to riches, homeopathy, theraputic touch, polygraphic lie detection,...  Many scientists would add the International Space Station as a instrument for scientific research and the Star Wars Missile Defense Shield.  (Hydrogen burning vehicles as a route to solving environmental problems is in a class of pseudoscience and scientific illiteracy of its own—see "What's New," the American Physical Society's Web commentary by Bob Park.) 

This pseudoscientific thinking which proves anything we desire fails to adequately consult the real world, and it sorts our desires into two boxes: the desires we can confirm, and those we can't.  One box if full; the other empty. The information theorist will tell us that our information then has zero information content.  The purpose of information is to guide decisions, to help select between alternatives.  A system with zero information content can't select between alternatives because it describes a system that has no alternatives. 

But this is pretty abstract stuff.  We need pretty good perceptions of the abstractions to readily recognize the errors—or we need ample technical learning and robust ability to apply what we've learned—before such errors become "obvious."  "Obvious" logic that goes unobserved can let others mislead us into absurd beliefs, and they can more easily deceive us.  So we want to develop some ability to see those "auras of error" sharply and clearly.  The deceivers will find it a lot harder to mislead us if we can see their auras. 

Both statements confuse necessity and sufficiency.  Necessity and sufficiency are mutually reciprocal implications.  (See how some well-educated people sometimes show confusion about implications by defining energy with "Energy is the capacity to do work."  POTATOES.)