The solution is invisible to some mathematicians!

The results of this demonstration rapidly build up as Da Vinci Days procede.  It's there for everybody to see, yet remarkably few notice.  Statistical things are invisible to a lot of people.

Statistics deals with two phenomena: uncertainty and complex, multiple-factor interaction.  In the past couple of centuries, modern science made huge advances which opened up these things to human understanding and usefulness.  Statistics is a powerful tool that is seen by far too many people as nothing more than a tool of liars, cheats, and politicians.  It's power remains invisible.

Nevertheless, a large fraction of participants still do not recognize that the heights of the columns in the tubes constitute information that one choice gives half the probability of winning as does the other choice. Because a very large percentage of scientific information is statistical, scientific literacy requires that we look for and recognize such information.  Public education for science is failing at some of its important duties.

The photographer with his camera is standing between the two boys.  So why is he invisible?

This puzzle might seem to be trivial.  Far from it!  Our love of ranking everything by puting things in a line and looking to where things are positioned with respect to each other is almost always a very serious oversimplification.  Correct organization calls for ordering in many dimensions--virtually always.  MORE

Skilled magicians make the solution disappear.

Covering the checkerboard with dominos (or not covering it) demonstrates one of the great, almost invisible, truths of science and mathematics.

This puzzle's solution is "elegant."  Elegant puzzle solutions are evidence of kinds of knowledge that are a bit different from everyday expereience and having the slightly more abstract nature that makes up most of science and math.  Adequate science education must develop a sense of elegant answers.   MORE

See the invisible worms under the skin of your hand.

Visitors paint abstract patterns.
Other visitors look for images that weren't intended by the abstract painters.

Another elegant solution.  If we don't see these solutions, we may convince ourselves we are free to make arbitrary choices and can't be told we are wrong.  We can be wrong, and we need to understand why and how.

This high-efficiency fluorescent lamp has four bright spectral lines in the visible part of the spectrum as well as s continuous band of visible light

The spectroscope sees color as would an animal with an infinity of different cones in its eyes--one for each and every wavelength.

The spectroscope sees the difference between "line" spectra and "continuous" spectra, a distinction invisible to human eyesight. 

A lot of science became known when humans found a way to see this bit of the invisible.

Here is a simple device by which we can get some of the same information seen by the bee.  But we must be cleverer than the bee.

We rotate the polarizer until the blue sky is the darkest it gets.  The line on the disc then points to the sun.  If the sun is 90º away from our line of sight, the darkening is the greatest (the light is maximally polarized). As the angle to the sun is greater or less than 90º the darkening is less.  At 180º  (and at 0º) there is no darkening (the light isn't polarized).

Stereoscopic images are often felt to be illusions.  But they are no more illusions than are any other photographs.  Photographs send to the eye the same messages the eye would receive were it actually at the scene.  Stereoscopic photos do the same.  In the anaglyph, red and cyan images are printed on paper and received correctly by the right and left eyes because the glasses filter out the inappropriate images.  The phantogram stretches the printed anaglyph images out to the rear so that the images are sent to the eyes from a horizontal plane rather than from a photo held the way we usually hold a photo.  Stereoscopic objects rise up out of the paper and look startlingly real.