Teaching, learning, and understanding -- examples are critical, not just in school, but in life and at work.

After all, we all have to sometimes teach and sometines learn -- it's part of being a social animal. And we frequently have to think. So we should know how to do them well.

No matter what -- Acid. Base. Titration. Redox. Quantum mechanics.  Maxwell’s equations.  Navier-Stokes equations. Turbulence. Government. Psychopath. Discipline. Friend. Money. Honesty. Integrity. Reason. Logic. Induction. Deduction. Wisdom. -- in forming concepts of these things and understanding them, we should have examples, preferably a wide, varying range of examples. 

Here are two cases where I've used examples to teach concepts and understanding of them.

I. Adjectives
noun
cat, human, wisdom, reason, emotion, victory, oak, butterfly, friend, physics, grammar, philosophy, logic, steak, hamburger, home, school
--> a noun is a word that names a person, place, or thing

verb
think, understand, feel, run, throw, lift, jump, cook, eat, digest, rest, sleep, move, is, was, smells
--> a verb is a word that names an action or state

adjective
red, blue, big, small, fast, slow, strong, weak, wise, unwise, capitalistic, communistic
his, her, their
three, five, most, all, some, none
this, that, a, the
--> an adjective is a word that modifies a nout

adverb
slowly, quickly, wisely, intelligently, unsmartly, very, so
yesterday, yesterday, tomorrow, on my birthday,
here, there, on the corner, under the roof
for the team, because I said so, 
--> an adverb is a word that modifires a verb

preposition
through, to, out, upon, because of, in, over, across, in spite of, up, down
--> a preposition is a word that connects a noun to the rest of the sentence

The Adjectives Questions
Which one(s)?
What kind?
How many?
Whose?

The Adverb Questions
How?
When?
Where?
Why?

Notice some logical features in what we did. We identified these things:
What are they?
How are they similar?
How are they different from related things? What’s the contrast?
What’s the context?

We should do that in forming concepts of other things, and in understanding those things.


II. Projectiles. 

horizontal: ball pushed on ground, etc.
vertical: ball dropped, etc.
projectile: rock thrown, coin flicked off a table, cannobal fired, bulllet fired
self-propelled: bird, jet airplane, helicopter
affected by air resistance: feather dropped or thrown, piece of paper (not crumpled) dropped

Galileo: just as ramp/incline slowed down free fall so he could study it, so also a ramp slowed down projectile motion so he could study it. 

Notice some logical features in what we did. We identified these things:
What are examples?
In contrast to what?
What is definitive? How do we characterize it? 
Why do they do what they do? 
How can we understand it?

We should do that in forming concepts of other things, and in understanding those things.

Galilean Spiral: 
i. https://mathcurve.com/courbes2d.gb/galilee/galilee.shtml
ii https://mathworld.wolfram.com/GalileanSpiral.html

Kepler's Laws
https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion


Examples are key in forming concepts and in studying the things for understanding. And it is in the real things where we find their rich variety and all sorts of actions and causation. And it is in focusing on the examples that we stay tied to reality. 



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