"You can find magic in places you never thought to look."

Richard P Feynman (1918-1988), magician
enter the Feynman Web ring at the site by Bill Beaty

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)
Perception to Magic
Magic is what lies beyond the ordinary.
Magic: "...seemingly beyond human powers"  Merriam Webster Dictionary
1. Dimensions of color
Two retinal cones: blue-sensitive and green-sensitive
Protanopic vision sees this

To a protanopewho has two-component colorblind vision because it lacks red-sensitive cones "normal" human color is magic.

Three retinal cones: blue-, green-, and red-sensitive
while most others see this

To ordinary human color visionwhich has three components of colorthe six-component color of a bird is magic

Understanding of this abstract dimensionality of color vision was one of Feynman's magical insights.  (It's a remarkably difficult concept for most ordinary people.)

Here is Feynman's depiction of protanopic color
The Feynman Lectures on Physics I, p 35-8.

Knowledge for Use web site Use 'Back' to return.
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The outer rim of the diagram represents the pure spectroscopic colors. The "450" is the farthest violet that is visible (beyond which is ultraviolet.)  The "700" is the farthest red that is visible (beyond which is infrared.)   The inclined straight line at the bottom represents the purples, mixtures of red and violet.  Points inside the figure are mixtures of pure colors with white at the "C" region.

Two of the three "normal" human color dimensions are the X and the  Y of this diagram.  The third dimension is Z, perpendicular to X and Y: it represents intensity.

Protanopic color—all two dimensions of it—is represented by the family of red straight lines.  The "700" point is black. Moving away from "700" on one of those lines, a protanope sees the same color, ever brighter.

In 1958, Edwin Land described how two black-and-white photos could be taken that could be used to reproduce full color photos.  That seems to threaten the three-cone color theory of color perception.  At a weeky seminar, Feynman was shown the Scientific American article on Land's work, thought about it a moment, and said, "I don't think the three-factor theory of color is in any danger."  He couldn't say why, but a year later a computer analysis done at IBM showed that he was right.

2. Multidimensional measures
illuminating tensors
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 Lecture on Physics Vol II, p 31-1
Scalar measure
(one component only)

This is pretty much the only kind of measurement familiar to those outside of certain specialized branches of science or technology.  Nevertheless, it is usually oversimplification.

some people are brighter than others
When we get a feeling that there's something wrong with using comparatives and superlatives, we are beginning to understand why Feynman said, "...sooner or later you will need to use tensors."

Visually follow the development, "from infancy to science-see," of the increasing sophistication and power of human concepts of measure, HERE.

Tensor measure
(also vectors, complex numbers, quaternions,...)

Putting colors into an ordered array illustrates a simple vector measure: three components for ordinary human color, two components for protanopic colorblindness (deuteranopic, too).  Total colorblindenss is one component (scalar).  Bird color can have four, five, or six components.  Spectroscopic color has one component for each and every possible wavelength: an infinity of components.

When a surface reflects light, each wavelength will, in general, reflect a fraction of the light that falls on the surface characteristic of that particular wavelength.  That would make the "reflectivity" of the surface an infinite component vector, if that were the whole story—the vector could be represented by a graph of those fractions.  However, the surface might fluoresce: a given wavelength might also reflect at other wavelengths, too, like those bright orange detergent boxes on the supermarket shelves.  Each wavelength striking the surface needs a whole graph of its own showing the amount of all the wavelengths at which it gets reflected.  That makes the reflectivity of a surface a tensor. 

It's a rank-two, order-infinity tensor.

Color will be an unfamiliar example of a tensor to those who work in the "other fields" that Feynman spoke of when pointing out that the real world has tensors.  The most common tensors are properties of materials, the way materials interact with electric fields, magnetic fields, stresses and strains, for example.  And those who study such properties at a fundamental level must be familiar with the peculiarities of tensors.

The rest of the real world needs attention to multi-component measures, too.  Value of a human being.  Reward to a human being.  Cost of a product.  Benefit of a product—of an action, of a law, of a belief...  These all have multiple components.  Every time we imagine a line-up by "value," every time we rank anything to tell which is better, bigger, more valuable, or whatever, we are almost certainly oversimplying.  The oversimplification can be so great as to make our ranking virtually meaningless.

Sooner or later we will need to use tensors.  Or face the consequences of oversimplification.

3. What is energy?
More than half of today's science textbooks define energy with:
"Energy is the capacity to do work."
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
Aristotle's energy 
It's the colloquial "energy"
Aristotle coined the word "energy" from the Greek for "at work."  It's meaning is something we are all familiar with because we all get tired from work, especially heavy work—and we get hungry when we don't get food, thirsty when we don't get water, and drowsy when we don't get sleep.

Food (and fuel for the car) supplies what we "run out of"; it "restores energy."  This colloquial kind of energy is a kind of capacity for doing work.

What in the real world are they??
Science's energy 
It's Feynman's "energy"
During the nineteenth century, the science of doing work was developed into what got called thermodynamics.  A scientific concept of energy evolved, but this energy could be "unavailable for doing work."

Oh oh!  That makes "Energy is the capacity to do work" a logical impossibility.  But it's a logical contradiction that many textbook authors miss seeing.  Feynman not only sensed the contradiction, he saw far beyond it.

Feynman's picture of energy is something very abstract.  We have learned how to calculate a value for it in a lot of situations...and we have discovered that it is conserved.  As long as we take everything affected into account, it's total value doesn't change no matter what happens to those things.

They are very abstract...are they very real??

We call something "abstract" when it's something "apart from concrete existence," or when it's "theoretical; not applied or practical," or when it's "not easily understood." (All from American Heritage Dictionary.)

Feynman's magic was in the relam of the theoretical.  But, for him, it was in the realm of the practical: he could apply it with ease.  He could see it in the real and concrete world that he encountered day in, day out.  For the rest of us it was "not easily understood"—and often not understood at all.

But it worked.

Mathematician Kieth Devlin has a very simple resolution of what many might see as dissonance in these observations.  Those who, like Devlin and Feynman, have had a lot of experience working out mathematical problems will see those deeper abstractions as having a kind of reality of their own.  The abstractions are patterns in the real world.  They are patterns of patterns.  They are patterns of patterns of patterns of...

The distinction between green and orange is more abstract in a protanopic universe.
What d'ya mean,'TWO-TONE PAINT JOB'?
click on the house
'Your freshman year will cut out about a third of your class; the sophmore year will cut . . .' The reality of mathematical abstraction comes from the facts that a person who has "seen" the flash of insight that comes with "understanding"—Eureka!—can then recognize the pattern in previously unencountered situations, and can use the abstraction to help make things happen in ways they want.  "Once you've seen it, you can never again not see it," as Indian physicist, Vandana Shiva recently said, describing the "Eureka!" experience.
She also said "You can find magic in places you never thought to look."  Those who have yet to see those mathematical patterns have no sense of their reality.  "Theoretical" then is the realm of stabbing in the dark, blind to the patterns.  But the patterns are there for everybody to see—although perhaps not easily, for they lie in the magical realm at the edges of human comprehension.

The nearly universal pattern of learning that beginning students of science and mathematics follow is prodigous learning of specific instances of applications of the abstractions.  That makes it learning without understanding. It's hollow and almost useless.

abstract: Thought of or stated without reference to a specific instance.
(American Heritage Dictionary)

The power of science's energy concept come from its complete generality
...from it's freedom from human wishes or arbitrary decisions.
It's deep abstractedness is the source of this generality and freedom
...and the source of its difficulty of being understood.

4. The textbooks everybody learns from
Surely You're Joking, Mr Feynman,
Bantam Books
is a chapter,
"Judging Books by their covers."
pp 262-276.
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 


Feynman was asked by the California State Curriculum Commission to help evaluate all of the science textbooks submitted to the Commission for possible K-12 use in the schools of California.  Those texts occupied 17 feet of bookshelf space.  Feynman was the only evaluator diligent enough to discover that one of the textbooks had all blank pages between the covers.

As he read through the books, his wife complained that he repeatedly burst into shouts, "erupting like a volcano."  ALL of the books were UNIVERSALLY LOUSY. 

Those books have been the source of learned science for almost everyone in California...and probably almost everywhere else, too.  The authors of those textbooks are the teachers of our teachers.  Teachers and learners alike are learning something that goes by the name "science," but it is not science in the sense that scientists have learned...and understood.

And can use.

The May, 2001 issue of The Physics Teacher reports some recent efforts to improve science text accuracy.
See the publishers' response
Many school districts have instituted competency testing for all students.  Do the authors of the above texts write the exams?
Look at three Oregon test items
"Unscience" is frequently encountered in daily discourse.  The first step in constructing a theory of unscience, is to collect
common misconceptions

The Feynman Lectures on Physics contain many remarkable insights that will be found in very few, if any, other texts.  You will find many other references to these insights if you follow the above links leading to other pages of Explore the Physicist's Domain and Knowledge for Use.