A
Sheet

Links are to other sites
A puzzle sheet that demonstrates:

Answers often require new, unexpected ways of "looking."

...but when you "see," you may know something in a pecularly undeniable way.
Sensing:     "Chessboard certainty."
"Buzz-saw certainty."
"Potato certainty." 
"Potato certainty" refers to seeing something wrong with defining 'vegetable' with "A vegetble is a potato."

Human beings have a large repertory of "seeing" skills.

...and although all are aspects of "intelligence" they may not be related to "IQ."
Seeing:  Multidimensional webs of causes and effects
Multicomponent measure
Mutual reciprocity 

 Science sees subtle simplicities.

...but so subtle that those simplicities are seldom seen
Most learning remains:     Prescientific misunderstanding
Hollow
Useless 


 
Ask, 
"Did I learn science in a way that makes it useable to me?"

Think of something you learned:  Perhaps, "Energy is the capacity to do work."  Or "F = ma."    Or "Mass can be converted to energy according to the equation E=mc2."

Then ask, "Can I use that knowledge to calculate the value of something, or to predict something, or to solve some puzzling problem?  How much energy do I get out of a nuclear explosion and how do I get to use that energy?  What forces are needed to accelerate my car as I drive around the corners on a mountain road at constant speed?

Remarkably few people can use their scientific knowledge to calculate anything. 

The reason is simple: That learned science was not really the ground breaking truth discovered in the past and now taught in schools.  In fact, what gets learned is usually the previous understanding of nature that was really misunderstanding.  It just gets set in a new language that sounds like the science.  Very complex learning gets substituted for very simple understanding.

Science is basically mathematical and logical.  But even the simplest mathematics and logic is a bit more subtle than is usually realized.

Ratios and proportions.  Negation of negation.  Rates of change.  Exponential variation.  Multiple components within a measure.   Necessity and sufficiency. 

Understanding science, "seeing" it, requires new ways of looking at such simple things.  Learning science is most often seen as a heap of complex learning.  The path to useful science begins with understanding simplicity .  .  .
 

Seeing simplicity:


 
Puzzles come in a great variety of flavors.  Jig-saw puzzles.  Word puzzles.  Crossword puzzles.  Mathematical puzzles.  Logic puzzles.  Pun puzzles.  Some solutions are obvious.  Some are “obvious.”  Some are easy.  Some are un-easy.  Some are downright difficult.  And some…
...are downright sneaky!
Easy but sneaky...
  • What is the next letter? 

    • W T F S S M . . . 
    J F M A M J J . . . 
    O T T F F S S E . . . 
    A E F H I K L . . .
     

  • Rearrange the letters of NEW DOOR to make one  word. 
  • Two girls were born on the same day of the same month  in the same year of the same parents, yet they were not  twins.  Explain. 
  • "How much will one cost?" 

    • "Twenty cents," replied the clerk in the hardware store. 
    "And how much will twelve cost?" 
    "Forty cents." 
    "Okay, I'll take nine hundred and twleve." 
    "That will be sixty cents." 
     What was the customer buying
     
  • A wheel has ten spokes.  How many spaces does it have between spokes?
 
Not that easy...
  • 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 pices after each cut?
  •  Start with a chess board and 32 dominoes.  Each domino is of such size that exactly covers two adjacent squares on the board.  The 32 dominoes therefore can cover all 64 of the chess board squares.  But now suppose we cut off two squares at diagonally opposite corners of the board and discard one of the dominoes.  Is it possible to place the 31 dominoes on the board so that all the remaining 62 squares are covered?  If not prove it impossible.
  • Among the assertions made in this problem there are three errors.  What are they? 

    • 1.  2 + 2 = 4 
    2.  4 / 1/2 = 2 
    3.  3 1/5 X 3 1/8 = 10 
    4.  8 - (-4) = 12 
    5.  -10(6-6) = -10 

 
These are the sort puzzle that for 25 years Martin Gardner challenged us with in the pages of Scientific American.  They are fun.  But they also teach.  Furthermore, they can develop our ability to see things we didn’t know existed.

You can see many more fun puzzles that dig deep into our understanding of things we never suspected by going to: Eureka!

(Many of the above puzzles are reached by clicking  HERE.

 
 
Another kind of puzzle

Many things we “know” about science are the false beliefs that someone in the past realized were wrong and corrected.  We still “see” the misconceptions that the new discoveries replaced.  The new concepts are simple, but they are a little tricky.

...”Simple but subtle”...
  • For every action, there's an equal and opposite reaction. 
  • F = ma
  • Time is the fourth dimension. 
  • You can't simultaneously measure both position and momentum. 
  • Quantum mechanics showed that the world behaves according to statistical laws 
  • Mass can be converted to energy and vice versa:  E = mc². 
  • The uncertainty principle revealed that observation disturbs the observed. 
  • Energy is the capacity to do work 
  • Einstein showed that everything is relative. 
  • Temperature (or heat) is the motion of molecules; it's their kinetic energy. 
  • Gravity equals 9.8. 
  • According to the laws of physics—they're known as the first and second laws of thermodynamics and there are no known exceptions to them—you can't use energy more than once. 
  • Creation science is an alternative to evolution...and every bit as scientific. 
 Some of these are correct statements but are persistently misunderstood.  Some are simply wrong.  Some aren't even wrong. You can find some discussion of these matters at Knowledge for Use.  HERE.

You can find more details in one of the “secret” sections of that site. ( Look under the door mat of the front door for the key.)

Even more treasure hunting is found through the (invisible) Diamond Plover Egg wormhole-link at the front door of this site.

Investigate Oregonians for Rationality at
www.o4r.org

Be sure to look for “The Puzzle Zone.”