The Power of Explanation
the agony of powerless explaning
"You can find magic in places you never thought to look"
Vandana Shiva
Magic: seemingly requiring more than human power.
Meriam Webster Dictionary
Study Newton's laws of motion from a river raft trip.You can find magic in places you never hought to look.Entropy has many facets -- waste products being most salient.Five levels of abstraction -- perception to magicInformation is the currency of human interaction with the world.What is logically wrong with this drawing?
Knowledge for the birds
Creativity in Street Maps
Lotteries: traps for the gulls!
Who knows what magic lies in the brains of birds.
Birds have difficulty communicating their knowledge to humans.

A human sunbather basks in the sun on a hot, late afternoon.  Every day that week, after work, from 6 to 7 pm, she lay in the hot sun with no effect whatever.  Then, right after lunch on Saturday, she sunbathed for 15 minutes and got a bad sunburn.

The bird watching from her nest high in a tree knew something the sunbather needed to know, but would have had great difficulty understanding, even if the bird could chirp in fluent English.

The bird sees color that includes ultraviolet detection--and also has "dimension" greater than the human's paltry three.  As the sun drops toward the horizon it's color (to a bird) shifts from ultraviolet toward red.  The difference between noonlight and late-afternoonlight is as distinguishable (to the bird) as is the difference between green and orange to a human being.

So if a bird could chirp in fluent English, what could it say to the sunbather to explain what it's view of color looks like.
Good maps get you there; bad maps get you lost.
A correct map (dark) superimposed over a creative map (dim).  That grid of streets shows on many (most?) street maps of Portland. 

"That's a good map," said a city planner.  "It shows the dedicated streets that a city planner needs to know about."

"But almost all the people who try to use this map are trying to get from one place to another," I replied. "All those non-existent streets make the map useless for those people."

"It's a good map."

And a fourth-grader added, "It's a good map; I found all the street names my teacher told to find."

What could a map maker say to the city planner and to the fourth grader to explain what makes that map a really bad map?
ONE winner.
"If I buy the winning ticket,  I'll be set for life."
68,264,008 losers"But
if you bought one of the other 68,264,008 tickets, you lost the two dollars you paid for the ticket."

"So, I'll keep trying.  Eventually I'll win."

"The more times you play, the closer to exactly 45% of all the money you put down for tickets will be what you lost.  The Lottery Board already set your losses.  They can do that because they understand the statistics."

"Statistics is a tool of liars; I'll keep on playing!"

What could a statistician say to the gambler to explain why his gambling addiction is also a failure to "see" something that other people see as a completely compelling reason not to play those games.
"Math's not a democracy: she's right!"
All the Books
A hustler presents you with three boxes into one of which he places a valuable prize, but you don't know which one.  You get to choose one box and keep the prize if it's there.  You choose, but he doesn't tell you if you won.  Instead, he says to you "I'm going to open one of the boxes and show you what's inside."  He does (and you see that there's nothing inside), and then says, "Now, would you like to stay with your first choice, or would you like to switch."

Marilyn vos Savant presented this puzzle in her weekly Parade column, and explained why the chooser should switch.  Many professional mathematicians wrote back saying that she was wrong; in fact, more said she was wrong than said she was right.  However, one university Math Department head wrote, on seeing the math community's responses, "Math's not a democracy: she's right!"

What might that math department head (OSU's, I recall) say to the anti-Marilyn mathematicians to direct their attention to the places they never thought to look, enough attention that once they saw it they never again could not see it.  (Many of them devised computer simulations that revealed that she was right.)
Seventeen feet of books on the shelf
In the 60's, Richard Feynman was asked by the California State Curriculum Commission to help evaluate all the science textbooks submitted to the Commission for possible K-12 use in the schools of California.  Those texts occupied 17 feet of bookshelf space.
Feynman was the only evaluator diligent enough to discover that one of the textbooks had all blank pages between the covers.  As he read through the books, his wife complained that he repeatedly burst into shouts, "erupting like a volcano."  ALL of the books were UNIVERSALLY LOUSY. 
"Everything was written by someone who didn’t know what the hell he was talking about, … They were teaching something they didn’t understand, and which was in fact useless…”  All of those books were, "a little bit wrong, always! ... Perpetual absurdity ... UNIVERSALLY LOUSY!"
Surely You're Joking Mr. Feynman, pp 262-276
In 2002, John Hubisz reported that in a study of all the middle-school physical science texts, "Not one of the books we reviewed  reached a level that we could call 'scientifically accurate'..."  In Physics Today (May 2003) he wrote, "Thousands of teachers are saddled with error-filled physical science textbooks that fail to present what science is all about...
All the publishers of those books had been sent letters asking for their participation in the study.  Not one of them replied.

What might the invesitgators say to the publishers to explain why they should take an interest in the investigation
"We can, and we've got to, do better than this."
Theodore Seuss Geisel 


Here are some tantalizing tidbits to follow further:

Why the similarity between the words "theater" and "theory"? Everyone who uses "theory" to mean "guess" or "stab in the dark," when the word refers to a scientific theory, is displaying a glittering aura that says, to everyone who isn't in the dark, that he (or she) is in the dark about science.
"...we have no knowledge of what energy is." Feynman said that.  There's a ton of magic in that statement, and everyone who makes decisions about energy needs at least a little of that magic.
"...sooner or later you will need to use tensors." Feynman said that, too.  There are at least two tons of magic in that statement.

Protanopic color is represented by the red lines.


This, too, is a bit of magic from Feynman.  With a little thinking about it we can understand why, in the color cube below, so many adjacent pairs of colors don't look very different from each other--especially if they are blues or greens--while other pairs look very different.  (The differences in the digital color coding between any pair of adjacent cublets are the same as between any other pair.)


(Protanope, 9 on the left -- "normal," 27 on  the right.)

When we ponder over this diagram, we can see much deeper into Feynman's magic.  We can also appreciate much, much more that Mother Nature didn't do very well by human beings in the color vision department.  We just think she did because it's all we know. 

...Until we begin to see the science...

.. What are the dimensionalities of the colors in the three pictures?
The tulip is black to a human being, but to a bird it might appear brilliantly colored.  If the tulip reflects a lot of ultraviolet, it will.

If a bird tried to explain the tulip's color to a human being he (or she) would be just tilting at windmills.  Views of our surroundings from different eyes in different heads might differ more than we can understand.

Don Quixote, Sancho Panza and the bird: Who sees things of the real world?  Who sees a world only of his own mind?  Who sees things neither of the others sees?
From the high saddle of our horse: Do we see more than does the man on the ground? More than from the high view of the bird?  How can we explain to others what we see?