Da Vinci Days 2002 Oregonians for Rationality booth

Martin Gardner's Buzz Saw
..

 A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes.  He can do this job easily by making six cuts through the cube, keeping the pieces together in the cube shape.  Can he reduce the number of necessary cuts by rearranging the pieces after each cut?  Either show how or prove that it's impossible. A set of 27 small cubes was provided to let puzzle solvers try out different rearrangements after each pass of the saw.  Here we see the first slab cut off and then placed to take advantage of the second cut so that it will make a bit more of the needed cuts.     You will understand this principle better if you have at least tried to solve the puzzle before reading past here:

Another puzzle, "MAKE A CUBE" also conveyed this information:

"This puzzle has almost no secret at all.

It was simply to arrange 27 small cubes to make a larger cube that had all the same color on the outside (red or blue), and had all the inside surfaces white.

It does have a little bit of a secret...see below.

Here it is assembled:

The solution to the buzz saw puzzle is revealed by the center cube of this puzzle.  All its surfaces are white (the only one with all white surfaces).  All the white surfaces in the puzzle must be created by a fresh saw cut in the other puzzle.  All six cuts of the center cube must be made: five-cut (or fewer) solutions are impossible.
Before you see the answer to this puzzle, a five-cut solution seems at least a possibility.  But...
 Aha! When you see the solution it's not a guess. It's a certainty in a very special way. Nobody can show you it's wrong. If anybody tries, you know they don't understand the answer.

"Buzz-saw certainty"

Much of science is made up of concepts that have many points of Buzz-saw certainty.
Yet, these points often go "unseen," and the certainty is not recognized by many (most) learners of science.
A pseudoscientific idea is usually made up of concepts that have many "five-cut buzz-saw" elements.
Real science goes simply unseen, awaiting the hard work that leads to those buzz-saw certain insights.

 Now, suppose someone has offered a \$3000 reward for anyone who demonstrates a five-cut solution.  That’s a pretty good incentive to believe you have found that solution.  And there’s someone who claims to have done it.  He is certain he has.  The person offering the reward is just as certain he has not. One opinion is wishful thinking.   One opinion is logically correct (more than “just opinion”). Self-deception      vs    "She (Mother Nature) who must be obeyed"

So...
Always look again!
There's more than meets the eye.
and more, and more, and more, and...

Everyone can see some thing(s) that someone else cannot.

When we don't see one of the patterns of deeper reality,  we can easily convince ourselves it simply doesn't exist.
It's then we should  ponder those patterns we didn't see or susspect until, one lucky day
while we were thinking hard about some problem, it suddenly hit us:

EUREKA!...I SEE IT!!

Everyone can see more things, if they're willing to work at it.