It's from a list of "Children's Misconceptions About Science."

• Stars are evenly distributed throughout the galaxy.
• Humans are responsible for the extinction of the dinosaurs.
• Batteries have electricity inside them.
• Boiling is the maximum temperature a substance can reach.
• An observer can see more of his image by moving further back from the mirror.
• Any crystal that scratches glass is a diamond.
• Air and oxygen are the same gas.
• The metric system is more accurate than the other measurement systems.
• Cold is the opposite of heat and is a different substance.
• The more mass in a pendulum bob, the faster it swings.
• Seasons are caused by the earth's distance from the sun.
• Many, many more . . . (See site.)

An electrical engineering student in a differential equations course was puzzled by the following question:  "What if the temp is 4 degrees F outside, and then the temperature drops 7 degree.  What is the new temperature? "  When forced by his instructor's willingness to let the uncomfortable silence continue without limit, he finally answered, "Zero?"  The student had managed B's and C's in other math courses, but still had not mastered the exemplar most of the mathematically competent use for negative numbers: position on a line.  Nor had he learned the rituals he might have learned when appropriate "perception" of that line was lacking.

My student who rewrote "Energy can be neither created nor destroyed" to read "Anything created cannot be destroyed," and rewrote, "An object retains a constant motion in a straight line until a force acts upon it to change that motion" to read "An object has a constant motion until that motion changes," was rewriting physics to a lesser degree of abstraction, one that she could understand.  She worked very hard on those rewrites.  After the exams, she came to me and argued vigorously that her statements were better than the originals.  She could not understand the correct principles.  She was "blind" to some relationships which most adults have very little difficulty with. (This student had an identifiable developmental limitation - SEE)

And most of us were "blind" to the sources of the constant flow of "magical" insights–his "unique Eurekas"–that Feynman came up with in his seminars.

These seem to span a vast range of "intelligence."  And in a sense, they do.  But that is a sense we should pause at and contemplate.  It's a vast range from our human viewpoint.  But those different "intelligences" are all human.  It really isn't very far from the human invention and use of negative numbers to the human invention and use of tensors, a powerful mathematical tool that can shed just a bit of light on the knowledge a bird might get through six-factor color perception.  Negative number gets its power from our thinking of numbers as positions on a line.  Vectors extend that thinking to more dimensions: line, to area, to 3-D space, to 4-D space, etc.  Tensors extend that thinking by taking the step again; by iterating that step upon itself.  The mathematics of electrical engineering requires, at a minimum, some perception of the abstraction of negative numbers.  Seeing the egalitarianism of a humane society requires some perception of the abstract, higher-dimension spaces.  (I cannot begin to analyze what Feynman was doing when he solved differential equations.  It was totally outside the edges of my comprehension.)  The lowly (??) bird still knows something we cannot.

A short lesson from one of Nature's humbler creatures.

The "edges of human comprehension" are evolutionary development edges.  Science is—in some way perhaps barely recognized—awareness of and response to the realms outside our evolutionary development.  Buried in a delightful work of modern literature is a beautiful lyric description of this edge.  It is by Loren Eiseley in his set of essays The Unexpected Universe.  The essay is "The Hidden Teacher."      The "hidden teacher" was a spider.  Eiseley was walking up a long gulch "on a rainy morning in the West" when he encountered this orb spider, one foot on the signal strand of the web that would tell the spider when some meal got snarled in the web.  The world of spider was limited to no more than the "lines and spokes of the great wheel she inhabited."  Eiseley, and the world of human beings, were outside the edges of comprehension of spider.  "Spider was circumscribed by spider ideas; its universe was spider universe.  All outside was irrational, extraneous, at best, raw material for spider."      Eiseley tells of later haunting memories of that spider, as he thinks of us, with our spider web-like radio telescopes reaching out to hear the vibrations of the universe.  He asks if we, too, are not limited, like spider, to human thoughts, human ideas, . . . And he concludes, "It is no longer enough to see as a man sees–even to the ends of the universe.  It is not enough to hold nuclear energy in one's hand like a spear, as a man would hold it, or to see the lightning, or times past, or time to come, as a man would see it. . ."      Look at those "misconceptions,"  for they signal vibrations from outside human universe.  Human is circumscribed by human ideas; its universe is human universe.  All outside is . . . ??     This Web site tells of a little of what might lie outside.  You can learn what we have tried to tell.  But learning is not enough.  You must see.   In seeing, is the Platinum Plover Egg.     ...but where is it???

RTN