Science is recent in human history.  Millennia passed by before humans discovered these well-kept secrets of nature, these patterns of nature that Nature forgot to give us perceptions of--even though many other creatures see things we knew nothing about.

The knowledge of science, and the thinking that "sees" that knowledge, has a lot of power--and as long as we know little or nothing of it we will see those who can use it as "magicians" because magic is that which "is seemingly beyond human power."

The patterns of science are abstract patterns, but this merely means that we have to extend our perceptions to see them, with mathematics usually part of our tool kit.  Mastering math is a little harder (but a lot simpler) than memorizing a lot of facts, rituals, and academic lore.  Educators have greatly improved on the techniques for mastering math and science.  But their techniques involve some effort, some hard mental workouts...Forget cramming.  Get used to heavy puzzle solving; to the work and to the joy of surprising discovery.  Eureka!

Math can be our route to magic.


We all can develop our science-seeing intellectual powers, not by listening to explanations in lectures, but by "active mental engagement."

The route:

Discover the route 
 to magic
that which seems to be beyond human power 
Becoming a better magician
 that goes through 
man's deepest understanding of the patterns of Nature
...and of the patterns of patterns of patterns of patterns...
But it's not that drudgery, the "math" that turns everybody away.
It's Keith Devlin's kind of math!
and then, understand deception
deception is another route to magic -- perhaps it's the entertainer's magic
...but perhaps it's the magic which usually fails, self-deceptive magic.

Some Steps:

Consider this:

Science lets those who understand something of science do things that seem beyond human power.


For example:
Calculate the operation of rocket engines that will take a vehicle to Saturn, inject that vehicle into an orbit that passes through the Cassini ring gap, and then drops part of that vehicle onto Saturn's moon Titan.

Newton's three laws of motion, dating from the 1660's, have the directions, if not the technology, needed for this task.

Magic: seemingly beyond human power.
Meriam Webster Dictionary
Newton's laws of motion are learned by millions, but something is odd about most of that learning.  It's usually metaphorical, not mathematical; mysterious, not intuitive; learned, but not quite understood.  Using that learning usually seem to be a bit beyond human power. 

Newton discovered routes from the metaphorical knowledge to the mathematical knowledge and so set the course for science.  Those of us who came after Newton need to retrace those routes if we are to wield the power of the science seen by Newton. We reshape our thinking.

Mathematics is a step beyond metaphor and simple human language.  It deals with patterns at a deeper level of abstraction. 
Newton's three laws of motion are one of the physics teacher's favorite places to start teaching physics.  They were where Newton moved resolutely into abstraction deeper than metaphor and thereby moved mankind into the effective science we have today.

Physics students resolutely learn those three laws plus a lot of mathematical paraphernalia that seem to solve problems using those laws.  But the learning leans strongly toward rote and ritual.  The actual abtract relationships seen by Newton remain largely invisible.  Encounter a situation where the laws apply--and could give us their great power to make things happen as we wish--and those learners find they were not seers.  They don't recognize the laws; they don't see the magic; they can't use the science.

To see and use science, we must discover the routes from metaphor to math.  Then, and only then, we can become magicians.

Law # 1: An object retains its velocity or remians at rest until a force acts upon it to change its velocity.
The opposite, "motion implies a force" is believed by about 95% of those who have passed an elementary physics course.

Law # 2:  F = dp/dt -- usually learned as the approximation, F = ma where a is the acceleration associated with the force, F (p is momemtum = mv)
About 95% of students who have passed an elementary physics course give the wrong answer to this question: "What is the direction of the acceleration, up or down, of a freely bouncing ball at the bottommost point of its bounce, that is at the instant its velocity changes from down to up."  That 95% does not adequately understand acceleration.

Law #3: To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." 
The essence of this law about "action" and "reaction" is that forces are interactions between two objects, the force on one and the force on the other being merely two sides of the same thing.  Most students feel that that the law asserts that causes have effects and effects have causes, and never master enough of the skill needed to recognize and relate the intrcate interplay of multiple influences that govern everything we interact with.

If you know it, you can repeat it on a school exam.  But if you understand it, you can recognize when you need to use it:

...And you can use it.

to your advantage.
If the science remains invisible,
we might discover pseudoscence instead.
Law #1 requires recognition of multiple influences and their correct interrelationships; for example, it requires that we not improperly invert implications.
Law #2 requires the concept of the derivative, the extrapolation to an unattainable limit of a ratio; it also requires some sense of vector and multidimensional spaces.
Law #3 requires recognition of complementarity, separability in some sense but inseparability in some other sense; it also requires a good sense of multiple dimensions and influences.
(This is the magic of Piaget's "formal operations.")

Some frequently missed concepts

from APS*, via Larry Learner, thru Jerry M.
A body maintains
Its rest, or straight-line motion
Unless net force acts.
F equals p-dot.
That is all you need to know.
Use it with wisdom.
To ev'ry action
There's an equal reaction
*American Physical Society

Mathematical abstractions have a peculiar undeniability
that tells us they have answered some question in a very special way.
They have some "buzz-saw certainty," like the answer to Martin Gardner's buzz-saw puzzle.

Martin Gardner's buzz saw
Some different buzz saws
who, what, and why of this page
He considered this puzzle to be especially illustrative of the missed logic of pseudoscience. A series of certainties of increasing abstraction. Why we think this is important.
Who we are.

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