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?
A five-cut solution?
Up or down?
Who gets injured?
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!
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.
...and it's undeniable...
A larger look at
Normal human color vision
Three dimensions are needed.
and protanopic vision
The third dimension isn't needed.
from Martin Gardner's "Mathematical Games," in Scientific American
|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:
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?
|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
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.
|Many of the most common
errors of logic are mistakes concerning logical implication, the
If a person is making poison
gasses, then he possesses beakers and flasks.
people find it difficult to see much difference between these two satatements.
This path that starts with logical
error leads to a very common line of false reasoning.
"We must pass a law against possession
of beakers and flasks
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
"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.
"Science can't answer
the deep questions about life, therefore we need not study science."
"Physics underlies all
understanding of the physical world, therefore physics can answer all questions
about the physical world."
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.)