"You can find magic in places you never thought to look"
Vandana Shiva
Magic: seemingly requiring more than human power.
Meriam Webster Dictionary
Science is simple, but subtle!
The Simple, Subtle Secrets of Science and Math
are almost never what they seem at first.

Most science was discoverd by solving puzzles
...not by learning facts or mathematical rituals.

The things pointed to on this page are very simple.  But they are also very subtle.   They usually take a bit of hard work before we really understand what they mean...understand what they really are...   Then they can become powerful tools we can actually use. 
Just look at how much--and how easily--the lotteries and casios take from those who are blind to statistics.
Here are some puzzles, and some things to try, that have helped others look into new directions
...and see into places they had never thought to look.

Knowledge for the birds
Ultraviolet: the sun's radiation that tans and burns (humans).

Birds see it. 
Humans are blind to it.

Human evolution left out a lot of possible perceptions--so a lot of our knowledge has to come from clever extensions of the perceptions we have.

Who knows what magic lies in the brains of birds.
Humans are colorblind to the bird's knowledge of color.  The spectroscope (diffraction grating) shows us how little detail we actually see.
Black to us; brilliantlycoloredtobirds
We see a black flower; the bird sees a brilliantly colored flower full of colorful patterns
(We can deduce that ultraviolet, which we can't see, is what tans and burns by getting skillful with the insights of elementary logic: the stuff of Venn diagrams and truth tables.  These are insights that reveal relevance and irrelevance, one of the five steps.)

Try Wason's Card Selection Puzzle (a simple puzzle with an elusive answer) with a group of friends. 

Creativity in Street Maps
Are we sticks-in-the-mud for thinking creativity is inappropriate in this setting?

When we describe something, we have to pay attention to making it right and making it complete.  Drawing maps and using maps is perhaps subtler than we might think.  Why do so many errors go uncorrected year after year after year.?

click on the map to see more
Good maps get you there; bad maps get you lost.
Correct map dark; creative map dim.
Take your city street map out for a spin with some friends,  Keep track of all the errors you find.  Who recognizes the errors most easily?  Who denies the errors and why

Who sees errors of omission as error.  (If I have no interest in something why should my map show it just because someone else might want to know?  All those extra lines confuse me!)

Lotteries: traps for the gulls!
Statistics: a powerful tool in the hands (minds) of the shrewd swindlers, the unscrupulous scoundrels, and the cagey swifts (raptor types) out to catch gulls.

Statistics and math: powerful stuff.
Ratios and proportions: simplest of math.
Orders of magnitude: missed by most.
Math: our most powerful magic.
Master a little; gain a lot.

ONE winner.
1 winner

It's easy to sell us on anything that's nice to think about when we habitually stop looking once we've see what we like.

It's easy to prove anything is true to the person who stops looking once he is shown a bit of confirming evidence.

It's easy to justify anything we do if we don't look for the potential harm of doing it.

click on the pile of tickets to see further
68,264,008 losers
68,264,008 losers

Orders of magnitude of disconfirmation.
Predictable, inevitable outcomes.

"Math's not a democracy...
Statistics: a tricky trade that trips us up too often.  But it's not a tool only for the liars and cheats (see above).  It really works (like magic -- see definition of magic).

Statistical knowledge has its own rules, and those rules take a lot of getting used to.

Simple question; subtle answer A hustler presents you with three boxes...

One of the simplest, and one of the subtlest, of the simple but subtle puzzles.  Work hard to figure out why.  Just what is it that so many people miss seeing?

(One easy route to understanding.)

Math's not a democracy...

All the Books
Perpetual absurdity.
[NOT] scientifcally accurate

What is it about science that many of its teachers don't quite get it right?  Make collections of common errors and study them.  Look here -- and here

click on the picture to see more books
The whole country learns from these textbooks.
Pseudoscience: what we believe before the Eureka!!

 Book authors, too, often haven't had the "Eureka" experience.

Science is not what it seems at first glance.  Math, too... 

The world  is not what it seems at first glance.

...and so, we sometimes find magic in places we had never before thought to look,  and when we find it, we gain powers we thought were beyond human powers.

.many routes to magic

Follow these five strange subtleties further