Da Vinci Days 2005
July 16 & 17
Corvallis, OR -- OSU Campus
Science's INVISIBLE Heritage
Oregonians for Rationality booth at Da Vinci Days 2005

Here is some of what was seen and experienced:
see Da Vinci Days 2003 for more detailed information on specific exhibits and puzzles

The infamous Monty Hall puzzle in 2005

 Monty Hall, 2004

Monty Hall, 2003

Year after year, the simple Monty Hall puzzle reveals how easy it is to miss even simple logic -- how easy it is to be fooled into believing something that just isn't so.
Jeanine & Trish manning Monty Hall in 05
The filberts in the tubes tell a tale about human observing -- that falls short.

Science happened because we human beings discovered new ways to interpret what our perceptions reveal.  Science concepts are almost never obvious at first encounter.  We have to think, and think hard -- after making observations that reveal more to us than casual glances reveal.

We don't even need to know what the question was when we see the results of hundreds of people answering "Stay or Switch"?  Those filberts in the tubes tell us that "Switch" wins twice as often as it loses, and that "Stay" loses twice as often as it wins.

That observation is statistical.  Statistics is one of the most powerful tools of science.  It's also, like most of science, not what it seems to be when we give it only casual thinking, what it seems at our first impressions.  What's more, the very simple Monty Hall question is subtle enough that even professional mathematicians have frequently gotten it wrong.

Monty Hall...raw Da Vinci Days, 2002
Monty Hall...cooked a bit Da Vinci Days, 2004
Monty Hall...well-done Da Vinci Days, 2003


The Subtle Puzzles

 "Though this be madness, there be method in't"

Discovering some surprising solution to a puzzle can be among of the most delightful of human experiences.  It's the reason most mathematicians and scientists do what they do.

But puzzles, especially the subtle puzzles, are probably underused as a teaching tool: puzzle solving has been found to be virtually the only route to understanding the concepts of science and math.  Those who would learn science must follow paths similar to the paths of the pathfinders of science.

Rote memorization is the path to writing down pi to several significant figures, or entering a phone number on a cell phone, but rote memorization has led almost all science and math students to a head full of useless knowledge.

Subtle puzzles need to be a part of the life of those who would become users of scientific knowledge.

See understanding as the Physics Education Group at the University of Washington sees it.

See pi as one artist misunderstood the intent of one book publisher.

See users of scientific knowledge as seen by the Knowledge for Use project.

. Future presentations of the subtle puzzles will adopt lessons learned at this, and previous years', Da Vinci Days

The puzzle illustrates how even the most elementary math can carry powerful insights -- and that mathematical insights sometimes require efforts of unfamiliar kinds.
Eighteen pieces can be assembled into a cube in many different ways.  But these pieces were chosen in a peculiar way.  If that peculiarity isn't discovered, assembling the cube can be remarkably difficult.

Future presentations of this "Cantankerous Cube" puzzle will have three presentations: 1) a "raw" puzzle that merely asks that the pieces be assembled into a 5 X 5 X 5 cube; 2) instructions that suggest some ways to arrange the small "stick," 1 X 1 X 3 pieces; 3) instructions that lead the puzzle solver through the arithmetical principle that underlies the puzzle.

It's so simple--especially when it has only the six pieces--that its solution can be found without discovering its interesting arithmetic.  But it's surprisingly difficult for such a simple task.  Discovering why is a nice fisrt step toward seeing why even the simplest science gives us so much difficulty.
Nine pieces can be assembled into a cube.  But the pieces were chosen in a peculiar way -- and it's the same peculiarity the above puzzle has.  (Three of the pieces, small cubes, have been left out--empty spaces take their place in the assembled cube.)

Future presentations of this puzzle will give hints that lead the puzzle solver to the principle shared by this and the above puzzle.

This "Deceptive Cube" puzzle is a variant of the Soma Cube puzzle which was popular a few decades ago.  Soma has seven pieces that make a cube, and it has over a hundred different solutions.  This variant has six pieces to make a cube, but comes as a set of two puzzles, which...


Future presentations of this puzzle will present a variant pointing out that the pieces can be arranged into attractive three-dimensional patterns.  Perhaps amateur architects can vie for the most popular structure as voted on by the visitors.

An elegant solution.  It is also a "buzz-saw certain" answer to the puzzle -- it brooks no argument.  Anyone who disagrees with it either doesn't understand the problem and its answer or is redefining either the problem or reality.


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.

Another elegant solution...and it's the source of the term "buzz-saw certainty." 

Martin Gardner gave us 25 years of subtle puzzles in his "Mathematical Games" feature of Scientific American.  This one comes from one the earliest sets of those puzzles.  Few, if any, better demonstrations of the nature of scientific elegance can be found*.

This small model of the crystal structure of silicon (Diamond-Cubic structure) introduces the important concept of spatial symmetry.
This two-fold pattern is easy to find.  The square-pattern, 4-fold axis, is the hardest to find.
4-fold axes
3-fold axes
2-fold axis
This is the sleeper lying among these puzzles.  The principle, when seen, has a lot of potential for reshaping our view of the world because so much of our view lines things up for comparison.  Lines are almost always inappropriate: Multi-dimensional spaces present themselves to us and we see lines --  somewhat like a totally colorblind sees color.
"Arrange so that similarity and proximity correlate."
is very different from "Line 'em up."

Arrange the Athletes

...and the reality is actually tensor-like

The polarizing filters demonstrate many other interesting properties of polarized light, including glare reduction, seeing past reflection on water, the "Brewster angle," (which happens to be the angle of the cone of your vision of what's outside the pool when you lay on your back on the bottom of a swimming pool), construction of variable density filters, darkening the sky seen by the color camera, etc.
The polarizing disc instructions: 

Hold the filter next to your eye and rotate it while looking at a bit of blue sky.  The blue will darken and lighten as you rotate.  Rotate to the position that makes the sky the darkest possible.  The line on the disc now points to the sun.

You have determined the direction of the polarization of the blue light (made blue and polarized by "Rayleigh" scattering).  You will also notice that the greatest darkening occurs when the angle to the sun is 90o.  As the angle to the sun moves toward 0o or 180o the darkening lessens--no darkening at 0o & 180o

A bee's vision detects the  amount and direction of polarization--we have no way of knowing the bee's experience of that detection--and knows where the sun is even if only a small patch of blue sky is visible through the clouds.

*But do consider this one, which does have a definite numerical answer:  A wooden sphere has a cylindrical hole drilled all the way through from surface to surface with the axis of the hole passing through the center of the sphere.  The hole is two inches long.  What is the volume of the remaining wood?

Elsewhere at Da Vinci Days 2005

OMSI sends an emmisary
Celebrating Physics in the 21st Century

Gyroscopic Stability
Chinese yoyo
Atmospheric Pressure
Drum filled with steam.  Outside cooled with water.  Steam condenses. Air pressure is 14.7 lb/sq inch.  Area of drum = 3400 square inches.  Force = 50000 lbs 
Drum collapses
Water, water everywhere.
Gyroscopic Stability
dishes spinning on top of wobbly sticks
Yank the table cloth out from under dishes & sticks
Kinetic Sculpture Race
This year, two of the sculptures were walkers
But the sand dune was too much to walk!
Da Vinci Days 2000
Da Vinci Days 2001
Da Vinci Days 2002
Da Vinci Days 2003
Da Vinci Days 2004

Explore the Physicist's Domain
We have faith in what we know.

What d'ya mean, 'two-tone' paint job? What is that loud cracking sound...?
Click here to study auras.
Illuminating tensors
Up or down?
We have faith in what we know.
logic blindness
up or down?
concept blindness