A first step toward understanding science: the mysterious undeniable
Once you've seen it, you can never again not see it.

Two-tone paint job?
31 dominoes = 62 squares!...??
A five-cut solution?
To Knowledge for Use website
Up or down?
31 dominoes = 62 squares!...??
31 dominos?
31 dominoes = 62 squares!...??
Who gets injured?

You can find magic in places you never before thought to look.
The magic you might find in Portland leads you to many hidden clues to understanding science: LOOK!

Seeing science is seeing a lot of kinds of errors you never realized were possible.

How might a person who sees something know when someone else does not?

New page, Jan 23, 2003 . . .  subtle concepts . . . how to present them? Perception
A  man named Joe was painting his house with green paint, but he ran out of paint half way through the job.  So Joe painted a swatch on a stick with the wet brush and took the stick to the paint store.  He compared his stick to the cans of paint until he found one that matched, and bought it.   He finished the house painting with the new can of paint.

His neighbor, Mary, looked at the new paint job and knew that something was wrong.  She asked the proud painter,  "How come the two-tone paint job?"

"What d'ya mean, 'two-tone paint job'?"

The painter had "protanopic" colorblindness (but didn't know it).  Neighbor Mary had normal human color vision.   Protanopic color vision doesn't seen any difference between grass green and orange because the protanopic eye has only two of the three color distinguishing cones of the "normal" eye.  The red-sensitive cones are missing.

The color cube diagram below shows how the two kinds of color vision see the colors.  The colorblind person can come to understand the difference between the different ways he and his neighbor see color, but only if he delves into the depths of abstraction of the mathematics and science of color vision. 

His neighbor simply sees the difference.
...and it's undeniable...
A larger look at


Normal human color vision
sees this.
Three dimensions are needed.

and protanopic vision
sees this.
The third dimension isn't needed.
It's two

Spatial visualization
Someone also might know when someone else doesn't understand something that is more abstract.
Martin Gardner's buzz saw
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.
from Martin Gardner's "Mathematical Games," in Scientific American
...but don't click here until you've given it your best.
The solution to this puzzle is very simple, but it requires that we look at the problem in a certain way.  Until we look in that way, we don't "see."  Try to solve it first, and then follow up by going to Da Vinci Days, 2002.

A person who has looked and seen can easily tell when someone else hasn't seen.   While, "Everyone's entitled to their opinion," some opinions surround a person with an aura of ignorance that is obvious to the person who has seen.  The insight needed to solve Martin Gardner's puzzle isn't very deep, and most people will be able to improve their aura through their discovery of the solution:

"Eureka!  I've seen it!"

The level of abstraction might be deeper yet.
Someone who understands elementary physics might be able to spot when someone else doesn't.
Answers given to this question reveal a lot:

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?

To Knowledge for Use website
Answers to this question are revealing because it involves virtually no learning but instead requires understanding of the simplest underpinnings of the concept of acceleration   Most of physics is related to acceleration in one way or another.  Before learning a lot about physics, a person needs to be able to recognize acceleration as what it is in the real world and distinguish it from velocity and also understand that it is a vector quantity—its direction is the simplest aspect of its understanding.  Otherwise the learning about acceleration (and physics) is hollow.

Most physics students first learn a lot about physics and quite a bit about acceleration.  They learn a lot of textbook questions and a lot of answers to those questions.  Then, when they encounter a situation where some understanding of physics would be a real advantage to them...their learning turns out to be useless.  They simply had not understood what they learned.

The answer to the bouncing ball question is utterly trivial when we understand acceleration—the answer is actually given in the statement of the question!  (Like in "Who wrote Bethoven's Fifth Symphony?")  Here lies the reason for the slogan "Learning is not our goal, seeing is."  It's also illustrates the often-unseen logic that rejects "teaching to the test."

Nevertheless, a remarkably high percentage of graduates of first-year college physics courses give wrong answers to questions like this one, questions that probe understanding, making it obvious, to those who "see," that they don't see.  The simplest questions about physics are often the most difficult.

Click on the diagram to the right of the question to discover more.

Logic Relationships
And deeper...
Those with a strong sense of elementary logic often spot when someone else makes a logical error.
Many of the most common errors of logic are mistakes concerning logical implication,  the statement, "If___, then___."

If a person is making poison gasses, then he possesses beakers and flasks.
If a person possesses beakers and flasks, then he is making poison gasses.

 Many people find it difficult to see much difference between these two satatements.
Few recognize that the statements are logical opposites.
The first statement is perhaps credible; the second is logical absurdity

 This path that starts with logical error leads to a very common line of false reasoning.
For example, the chemistry example might take this course:

"We must pass a law against possession of beakers and flasks 
because beakers and flasks might be used to make 
poison gasses which might be used by terrorists."

Some people will sense a kind of glittering, bright and sharply defined aura surrounding the speaker, an aura of absurdity.  These people can probably articulate the errors; give them names, identify ways to correct them, suggest other errors that are related and will probably be made by the same people.  Many others will see the aura, but it's a little dim, and it's not quite clear precisely what the error is.  To some, the aura isn't seen at all, and the law sounds reasonable enough.  To more than we might wish, the aura seen is an aura of astuteness and reason, of leadership and resolve: "What a great idea!"


The error of the inverted implication, "If a person possesses beakers and flasks, then he is making poison gasses," is straightforward.  But there's another, more serious, error signaled by that "might be..."

 "Might be..."?  We need "is"!  At the very least, we want to see valid evidence, and evidence that meets the kind of requirements that empowers science to overcome mistakes of observation and logic, to expand observation and thinking into aspects and dimensions that often get overlooked, and to avoid self-deception,--and perhaps deception by others who want to mislead us. 

"Might be... " without evidence is a red flag that warns us that the Prove Anything Ploy (PAP)is probably being applied.  "Prove Anything" starts with the conclusion, and then seeks corroborations and rejects disconfirmations.  In a world much simpler than the real one, finding a bit of corroboration might be all we would need, but in the real world we must sort through and evaluate complex networks of causes and effects, intricate alternatives of possibilities, and powerful wishes fed by robust human imagination. 

That oversimplified world is the world of pseudoscience: astrology, remote viewing, telekinesis, precognition, magical pyramids, spoon-bending by mental effort, alien abduction, biorhythms,...  We should add other unsubstantiated beliefs, too: belief that the lottery is a reasonable route to riches, homeopathy, theraputic touch, polygraphic lie detection,...  Many scientists would add the International Space Station as a instrument for scientific research and the Star Wars Missile Defense Shield.  (Hydrogen burning vehicles as a route to solving environmental problems is in a class of pseudoscience and scientific illiteracy of its own—see "What's New," the American Physical Society's Web commentary by Bob Park.) 

This pseudoscientific thinking which proves anything we desire fails to adequately consult the real world, and it sorts our desires into two boxes: the desires we can confirm, and those we can't.  One box if full; the other empty. The information theorist will tell us that our information then has zero information content.  The purpose of information is to guide decisions, to help select between alternatives.  A system with zero information content can't select between alternatives because it describes a system that has no alternatives. 

But this is pretty abstract stuff.  We need pretty good perceptions of the abstractions to readily recognize the errors—or we need ample technical learning and robust ability to apply what we've learned—before such errors become "obvious."  "Obvious" logic that goes unobserved can let others mislead us into absurd beliefs, and they can more easily deceive us.  So we want to develop some ability to see those "auras of error" sharply and clearly.  The deceivers will find it a lot harder to mislead us if we can see their auras. 

Without better aura detectors a lot of people are going to be misled.

Here's a similar error:

"Science can't answer the deep questions about life, therefore we need not study science." 
(Science isn't necessary because science isn't sufficient.)

"Physics underlies all understanding of the physical world, therefore physics can answer all questions about the physical world." 
(Physics is sufficient because physics is necessary.)

Both statements confuse necessity and sufficiency.  Necessity and sufficiency are mutually reciprocal implications.  (See how some well-educated people sometimes show confusion about implications by defining energy with "Energy is the capacity to do work."  POTATOES.)


deuteranopic colorblindness
no green cones

It's two dimensional.
All the colors seen can be ordered into a plane.

Dimensionality is simple but subtle.
One of the magical discoveries awaiting those who look in places they never thought to look

 email us