Physics has been a continuous revelation of the vastness of our human limitations and of our unseen potential for making errors.  Our perceptions reveal to us no more than the wispiest of shadows of what we look at.  Our language balks at its attempts to express and communicate what physicists have seen in  their experiments and conjured by their equations.  Yet, the little that science has revealed of  the territory around these edges of human comprehension has catapulted us into a new age of control over Nature—and over other human beings.

Physics—and its foundation, mathematics—remains mystery to most who try to learn it.  Most give up too quickly, unaware that physics (and mathematics) teachers have discovered effective new ways to help their students "see" their occult worlds, and to comprehend—and use!—the power of that catapult. 

Those who abandon the pursuit of understanding often continue to believe that what their perceptions reveal is potentially all there is; that what their language communicates is The Universe; that all opinions, hypotheses, and aspirations are equally valid or possible; and that they cannot be deceived, by self or others.

Wake up!  It's a new age!

The Magic of Physics
It's the magic of math.
"Become a magician."
"Magic: seemingly requiring more than human power."
Merriam-Webster dictionary

You know it's magic when:
¤ Some "magician" makes something happen, and you're pretty sure that you could not do it.
Jerry Andrus
This kind of magic is skilled misdirection, skilled deception,
based on deep understanding of human perception.

But the magic in math peers past the edges of human comprehension.
It's perception of the deeper patterns in the world.
The magic in math

There are two kinds of geniuses: the "ordinary" and the "magicians."  An ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better.  There is no mystery as to how his mind works.  Once we understand what they've done, we feel certain that we, too, could have done it.  It is different with the magicians.  Even after we understand what they have done it is completely dark.  Richard Feynman is a magician of the highest calibre.

Mark Kac 
(in Phyics Today)
¤ The simpler thing is more difficult.
Most classes give about 85% correct answers to this common textbook problem.  The problem is intended to be a practical application of Newton's Second Law of Motion.
However, the very slight complication added in this question drops the correct answers to about 15%.  (The two problems are essentially the same.)
problem from Don Howard

Both of these problems ask for a calculation of the acceleration of some object.  On the other hand, the bouncing ball question simply probes understanding, at the simplest and most elementary level, of what acceleration is.
What is the direction, up or down, of the acceleration of a freely bouncing ball at the bottommost point of its bounce, that is, at the instant its velocity changes from down to up?

This question is so simple that it answers itself.  Nevertheless most classes give about 5% correct answers if they haven't learned the answer to this specific question; that is, if they must rely on their understanding of acceleration.

¤ Even "experts" sometimes get it wrong.
A PBS series on psychology once discussed colorblindness.  They illustrated full human color vision, total colorblindness, and two-cone colorblindness with pictures like these:

normal color

totally colorblind

2-cone colorblind
The issue is dimensionality.  The producers of the series demonstrate lack of understanding of dimensionality.
normal color

All colors plot in 3 dimensions
protanopic color (no red cones)

All colors plot in 2 dimensions
The all-blue picture is one-dimensional.
"Energy is the capacity to do work."
a definition used by about half of elementary physics texts.
(Even those which speak of "energy unavailable for doing work.")

Definition requires logical (Boolean) equivalence, and a magician will sense that this definition fails to meet that requirement--in the way "a vegetable is a potato" fails.

It is important to realize that in physics today, we have no knowledge of what energy is.
The Feynman Lectures on Physics Vol I, p 4-1

Energy has a colloquial (Aristotle) meaning and a science (abstract) meaning.  Feynman states that about all we can say of science's energy is how to calculate it and that it's conserved.

Energy: once used can't be used again: like food and fuel
Quantum Leap: humongous change
Heat: temperature
Parameter: perimeter
Field: an invisible force
Light-year: a humongous time
Acceleration: increase of speed
Crystal: faceted and glass-like
Statistics: a tool of liars, propagandists and politicians
Epicenter: the center of something big
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


¤ You suddenly see it...and you know it's right.  You know it will work.
And you know you're a bit closer to being a magician yourself.
Monty Hall's choice 

People choose, "Switch" or "Stay."
The correct choice is shown statistically.
Do more people choose the winning or the losing strategy?

The magic is in how we think about it.

18 blocks form a cube
In many different ways.

But it's very easy to erect a barricade to a solution.

The magic is in simple arithmetic.

...but don't click here until you've given it your best.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 pieces after each cut?  Either show how or prove that it's impossible.

When you don't see the answer, you may wallow in a mud bog of complexity.  When you see the answer, the mud suddenly vanishes and you have no doubt.  The answer is extremely simple.  And the answer has "buzz-saw certainty."


The magic is in how we think about it.

...but don't click here until you've given it your best.
Arrange the athletes so that position and similarity correlate.
Physicists always have a habit of taking the simplest example of any phenomenon and calling it "physics," leaving the more complicated examples to become the concern of other fields...  Since most of you are not going to become physicists, but are going to go into the real  world...sooner or later you will need to use tensors.
The Feynman Lectures on Physics Vol II, p 31-1
The magic is in Hilbert space.
illuminating tensors
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Knowledge for Use
Learning science is only rarely understanding science.  Science that is not understood is not useful. 

Today's science results from unusually effective thinking that, among other things, sorts relevance from irrelevance, fends off self-deception, and recognizes patterns which must not be denied...but often are denied because they are not "seen."  Science is useful because it works—but it needs to be "seen" before it can be used.

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The magic of physics reveals a little of of what lies beyond human perceptions and easy comprehension.  And understanding it might be necessary to avoid errors, possibly very serious errors.  But understanding requires hard work:  "Don't shirk hard work...Learning is not your goal, 'seeing' is."

In America, (and elsewhere?)
the perceived importance of physics education has been declining for several decades.

"This is not suitable bedtime reading not if you want to fall asleep, that is.  Those who think that public policy should be based on sound science will be left in despair that such a goal can ever be reached in the midst of the competing political interests endemic to modern industrialized democratic societies, exacerbated by scientific illiteracy on the part of both leadership and electorate."
Paul M. Grant, reviewing
Politicizing Science: The Alchemy of Policymaking
Nature 18 Oct, 2003, p. 663
"You can find magic in places you never thought to look."
Vandana Shiva,
a physicist from India