"Once you've seen it, you 
can never again not see it"
"You can find magic in places 
you never thought to look."
Science has already helped you by making possible:
The computer you're are using right now
The telephones you use (too?) frequently
The television that brings you so much of what you know
The electricity that powers all that stuff
The efficient engines in your cars
The orthoscopic camera that can guide your doctor's hands
The polling techniques that can guide skilled spin doctors
The powerful instruments of destruction that can kill your enemies
The International Space Station that can....???

But do you understand what science did?

.Science sees patterns our perceptions miss.
Think about it:
How do we know what another person (or animal) sees?

For example:
Some people are colorblind:

.Total colorblindness
intenisty only
no red-sestivite cones
three kinds of cones

Blue-sensitive-cone-only vision sees this
Protanopic vision sees this
Normal humanvision sees this
Some animals have color vision which requires more than three dimensions.
Order all the colors seen
One dimension
Order all the colors seen
Two dimensions
Order all the colorsseen
Three dimensions
More dimensions
How can we know that?
 Here lies the magic of mathematics.


Update: 8 April 2004
Nature, vol 429, pages 596-7
In the 70's, birds "were reported to have 4-, 5-, or 6-dimensional color," some of which might be due to colored oil drops on the retina.   A news feature in this issue of Nature is more specific, "...birds have an extra class of photoreceptor cone cell in their retinas, in addition to the three -- sensitive to red, green, and blue light, respectively -- that we possess."  Those fourth class of cones are sensitive to the near-UV, 320 - 400 nm.  One outstanding mystery to the human mind, associated with bird 4-cone color, is the question, "What could the fourth Munsell dimension possibly be: after hue, saturation and brightness?"  Birds see it.
Magic color
The color seen by a bird with 4-, 5-, or 6-dimensional color is beyond human evolutionary development.  Without mathematics we have no way to think about it.  No way to ask questions about it — or to answer them.

The color seen by a person with "normal" human color is beyond protanopic or deuteranopic vision in much the same way.

Sometimes the green-sensitive cones are missing
Light Magic
Isaac Newton discovered that white light can be separated into light of many different colors.  That discovery was a beginning — it has led to many realizations that past our perceptions lies a universe of magic we can never see with our eyes, but can know by stretching our minds.  Human beings found magic in places they had never before thought to look.

Science found in the light spectrum a way to know the composition of the sun and the other stars.  The quantum, and its "jump," was discovered because science felt a need to explain the discovery that the spectrum of sunlight has dark lines within it.

Any color which is seen with vision beyond our own has a quality of magic to us in the same sense that Richard Feynman "worked magic with mathematics."  Any person who "sees" with perception beyond our own plucks out of a world beyond our comprehension some magical knowledge which actually works in the real world.
The atom and its structure were discovered, and understanding the nature of its nucleus led to human ability to see images within a living human body.

But not many human beings have seen how and why it must be that once seen, some insights of science can never again be not seen.  The colors seen by the "normal" human eye is but a wispy shadow projected from a space of not three, but infinity, dimensions—and birds know merely by looking a richer kind of color we can learn about only through mathematics. 

Color magic is in its

Science magic is in


Two dimensions,
but a different two


The subtle, magical mathematics of dimension lies in terra incognito for all but a few.  The patterns of mathematics are patterns of patterns of...  We call them "abstract."  Before we see them in that special way, we feel they are wispy shadows of imagination—mere specters from out of nowhere.  The quantum jump is so magical that almost everyone has yet to see what it is, but instead think of it as something that is its very opposite—after converting "quantum jump" to "Quantum Leap."  The atomic nucleus is so mysterious that many people think of it as the new-cue-less. 

Cue-less to the simple magic of mathematics remains the sad state of much of our New Age of humanity.

If that bird realized what we humans think of as color, it might think us a bit simple and silly!
Science is an art of not seeming silly,
To someone who sees something we've missed.


Mathematics is the science of seeing,
Those things we never suspected exist.


How might we know that we know?
Some examples of insights from deeper and deeper levels of abstraction—abstractions that often seem "not real" until that necessary flash of insight happens.
Look again — things are not what they seem
Words that are often misused by authors, journalists, advertisers, science students, and even an occasional textbook author.  The science meanings are not seen.
"Once you've seen it, you 
can never again not see it"
"You can find magic in places 
you never thought to look."
Secret of Science
(it goes by many names)

Flash of Insight
"She Who Must be Obeyed"
Dodging self-deception
Logical Imperative

Secret of Science
(it goes by many names)

The fourth level of abstraction.
Patterns  of patterns  of patterns of patterns  of...
Intellectual curiosity
Hard work


Correcting oversimplifications carries more weight than most advocates realize!

Six Sinister Oversimplifications