Powerful tools that too often gather dust in the attics of our minds

 
These tools are like telescopes and microscopes that extend our vision
It's up to us to dig them out of the attic, clean up their optics, and set their adjustments
For example:
Recognize
multiple
influences
Forget that "The Cause"!

Look for many causes...and many effects—that interact in intricate ways.

A good exemplar is the ordering of colors.     Follow this link

I didn't knock over the vase while my sister and I were fighting; she did.

We didn't cause that war; they did.

Guns don't kill people; people kill people.

Ferret out
relevance & 
irrelevance
What's important, and what's not, is often no clearer than "obvious."  And that means it's often unobserved. Watch all those people trying to get a sun tan on a warm summer evening...and not noticing that it's not working.  (They are thinking, "It's the heat.")
Recognize
symmetries;
mutual reciprocities
Seeing symmetry is often taking the view from "outside."  From the "inside" we easily fall prey to the "____centrisms" : ego-, ethno-, anthropo-, etc.  From the outside, we are more likely to see the implications of mutual reciprocities. The fist hits the jaw.  There is a symmetrical interaction between fist and jaw, but there is also a tendency to feel that the person who took the aggressive action gained some kind of immunity to damage.  POW!

Mutual reciprocity is the key to the puzzle about pushing on clay.

Recognize
commonalities
(abstractions)

Classification is a simple abstraction. 
 
 

The inverted implication is a more sophisticated abstraction.

Classification: animal, vegetable or mineral.  Animals have characteristics in common that vegetables and minerals do not.

The error of "Energy is the capacity to do work" has characteristics in common with not seeing why we need not turn over the "B" card when Wason's card puzzle is stated "If A then B."  Wason's cards.

Sense when, and how, to
extrapolate
(to unattainable limits)
The continuum is an extrapolation to the limit of the line containing every imaginable number lying between any two numbers, no matter how close to each other.  Quantum mechanics was the discovery that this is not the case. One of the more important extrapolations to limits in physics is that used to conceptualize velocity and acceleration: See.
Recognize the subtleties of
statisitcs
Many elements of insight are needed here:
Randomness. 
Extrapolation to limits. 
Ratios and proportion. 
Orders of magnitude.
Gambling.
Orders of Magnitude.

 
 
Navigating Second Glances
Return toScience is...

Look!  It's a square....No!  It's a circle.No!  It's a triangle.

Note: This page is an alternative view of "Some Goals to Aim At," 
          which is an alternative view of Piaget's "formal operations."
 [GOals]
"Complex things need many different views from many different
directions before understanding finally dawns."
And yet another view is HERE.