Oregonians for Rationality will set your mind to spinning at Da Vinci days in Corvallis Oregon.

One of the most popular demonstrations, especially with the younger visitors, is the Human Kaleidoscope, a huge prism of mirrors in an equilateral triangle that gives you a view of hundreds of yourself.

It spins.

It spins fast.

It spins slow -- most older visitors prefer the slower.

A small metal cube dropped down a small aluminum chimney.  But it takes its time falling.
Too much time.

Let's watch it fall in that 45 degree mirror underneath the chimney.

It floats leisurely  through the space inside the chimney.
It falls normally once it gets through.

Or do you?

Let's look at that again.  The eye can deceive when the mind doesn't quite get it right.
 
 
 
 

Stare at the center of the rotating wheel.  Just relax and let the hypnotic spell come over you.  This "Trizonal Space Warper," invented by magician Jerry Andrus will let you see into the magic of your mind. 

Relax.      …    Relax…     Let the magic come out.
 
 
 

Jerry's "Paradox Box" can be made by everybody to take home.  Here is a complex variation of the Paradox Box.  Watch that ring move over the box. 

The Paradox Box is not what it seems.

All of the puzzles can be found on the explorepdx.org website.  Just click on DaVinci Days 2003.  Explorepdx will show you many ways puzzles can give you insights into the mytsteries of science.
 

The infamous Monty Hall puzzle.  It has puzzled many professional mathematicians.

"I'm going to hide this here little ducky...

"I might put that little duck in number 3, or I might put this little duck into number 2.   I could put it into number 1.

"Which one do you think it's in?"
[Chooses number 1]
"Would you put your nut on number 1...Thank you very much.

"O.K.  Now I'm going to give you a chance to change your mind.  I going to make it easier by giving you a look in this empty one.

"Do you want to switch or stay with your choice?

...hmmm...What to do?"

"Stay."

"All right, she's going to stay.

"Is there a duck?  I didn't see the duck.

"That's all right though; you're still a good statistic.  You get to put [your result in]"

The String Thing.  If you've mastered your beginning physics course…forget it.  It won't help you much to predict what this little wonder will do.  It was invented at the Exploratorium in San Francisco, and their Web site will tell you what a couple of Nobel physicists have to say about it.  Explorepdx.org will direct you there. . . and tell you where you can get one of these for yourself.

Oregonians for Rationality wants everyone to:
 

• Find the fun in science.
• Discover ways to recognize the real science and to detect the un-science.
• Become able to use some of the great powers of scientific thinking.

The illusions point out that things are not always what they seem.

The magic points out that we can all be deceived;  sometimes we might even deceive ourselves.

The puzzles point out that answers to problems are often found in places we never thought to look…

And that those answers are often of some kind we never suspected exists.

Six pieces go together to make a cube.  The six-year old that just did it had no trouble.

The six pieces in the box look a lot like the old Soma cube puzzle which can be put together to make a cube.

But this puzzle is actually 12 pieces, the six in the front box and the six in the back box.  Those in the back box are the mirror images of those in the front box.  We can interchange any pair of similar, mirror-image pieces giving us a new puzzle.  That's what happened here.  There are twelve different puzzles, and one of that twelve has no solution. 

This puzzle solver had earlier solved one of the eleven that does have a solution.

And then, the deception.

That's the move there…when he moved one of the little stick pieces, he immediately moved another one of them in a certain way.  There are three of those pieces, and those three are the key…the key to solving this puzzle.  Trial and error almost never works.

This is a remarkable puzzle in that it is almost impossible to solve without its logical key.  This smaller puzzle has the same key, but having so few pieces, its solution comes with trial and error fairly easily.

Puzzles can illustrate some of the steps that can help anyone get a better and more useful grasp of science and math. 

Consider five good steps that have great potential for improving views of what science is.

Scope - Relevance - Math - Logic - and Tensor
 
 
 
 
 
 
 

As we climb the steps, as our viewpoint improves, we begin to see that some of our really great ideas are seen to have some really great problems.
 

•  The evidence for them was pretty flimsy; more wish than evidence. 

• When looking at our evidence, we imitated ad writers, spinning all we saw to make our wishes seem true.

• Our ideas contradict all of science, science we didn't at first understand; understanding squashes the ideas like bugs under our boot. 

• Our thinking contradicts itself...oxymoronic.

Step 1:  Scope.  Seek the truth, of course, but seek the whole truth.  Take it all in.

Don't just think about that winning lottery ticket.  Think about the 67,394,283 losers, too…and give each and every ticket equal weight.

Step 2:  Relevance.  Some things that attract a lot of our attention are simply irrelevant.  The sun is hot, the air is hot, and people are lying out in the sun to get a tan or they're avoiding the sun to avoid getting sunburned.  Temperature is irrelevant to sunlight being able to burn or tan.  Ultraviolet radiation is what does the job, and the amount of ultraviolet is very dependent on the angle of the sun.  For the same reason that the sky is blue.

Step 3:  Math.  Start simple.  Converting inches to meters, ounces to liters, dollars to Euros, barrels to gallons, watt-hours to BTU's, firkins to pottles.  Then master some of the more powerful math.  Discover the route from metaphor to math.  The energy we think about most of the time is metaphor.  The energy in science is math.

• ...like choosing the wrong door and cutting the odds of our getting the prize in half…
• ...or not realizing that which corners we cut off of that chessboard makes a difference of whether or not we can cover the squares with dominoes...
• …or the mistake of putting those key puzzle pieces in the wrong place. 

Step 5:  Tensor.   Did you say tensor?  Isn't that a bed lamp? 
 
 
 
 
 

In the Feynman Lectures on Physics, Richard Feynman suggests that most of us will have to use tensors, sooner or later.  Tensors are measurements that aren't complete and useful until we've gathered several parts of the measurement and put them together.  Who is the biggest athlete?  The basketball coach want the tallest; the football coach wants the heaviest.  Putting them in a line by size is actually impossible…
 
 

for the same reason that organizing colors in a line is impossible.
 

All of those "it depends upon" things which complicate our lives make lining things up for comparisons too simpleminded.  Ranking things in many dimensions is the right thing to do.

So visit explorepdx.org and see what Oregonians for Rationality have been bringing to Da Vinci Days for the past four years.  Then surf the explore the Physicist's Domain section of the Web site and see a little of what makes science work.  It can work for you.