PERCEPTION . . . IMAGINATION . . . METAPHOR . . . MATHEMATICS . . . MAGIC
Knowledge for Use

Learning science is only rarely understanding science.  Science that is not understood is not useful. 

Today's science results from unusually effective thinking that, among other things, sorts relevance from irrelevance, fends off self-deception, and recognizes patterns which must not be denied...but often are denied because they are not "seen."  Science is useful because it works?but it needs to be "seen" before it can be used.

Have you ever seen something that someone else obviously does not see?  You know that it's not "just a matter of personal opinion."  You know that if you act on what you see you have an advantage over the person who does not see.  (A puzzling example.) And if you do act on it, that person just might feel that you are using some kind of magic.

Welcome
to the
Perception to Magic

domain of PDX


An idea for exploration
We want to explore some ideas expressed in Keith Devlin's book The Math Gene.  (He's "The Math Guy" frequently heard on NPR.).  Devlin explores the roots of mathematics that are entangled in our ability to use language. 

As we humans evolved, we developed perceptions that let us see many kinds of regularities and patterns which give us knowledge that lets us interact effectively with our surroundings. 

But we also developed "off-line" thinking which lets us imagine things not currently being perceived, not currently directing our behavior.  Our brain also developed some ability to trigger itself in ways that led to metaphor (like the metaphor we call "energy"), and that led to language, representations of the world around us, and that language has certain organizing structures.

metaphor (Lakoff Principle)
We can sometimes recognize some of that organization.  We "see" certain patterns within our language, within our representations of the world.  We recognize these patterns of patterns.  Here lies mathematics.

We tend to feel that what we perceive and imagine is the world, in spite of the fact that we constantly discover new things.  The world is what we comprehend...or so it seems.  But some of those new things of modern science—like the mysteries of quarks and the mysteries of quantum mechanics—just don't make sense to us: we don't comprehend.  It's magic.  It's beyond those evolutionary developments by which we "see."

However, Devlin warns us not to shy away from mathematics, not to think it's "too hard a subject."?it's not math we hate, but rather some boring drudgery inflicted on us in math classes.  Mathematicians, too, hate that drudgery.  Real mathematics is a beautiful experience that comes naturally to us, as does language.   Mathematics is a search for patterns.  It's a delightful discovery of patterns.  And we all can do it.

The above in fable form: HERE


Some growth of scientific thinking — from infancy to science-see

Patterns

?-- easy       This dimension is abstraction --->       difficult --->   (the human evolutionary path)
primitive
a few other critters
only humans
a stretch for us
beyond comprehension
even worms do it
even plants do it
(a bit)

LOOK!
VISION
HEARING
TOUCH
HORMONES

PERCEPTION
JUST
MAYBE...

?????

SENSING WHAT MIGHT BE
 

IMAGINATION
TELL ME!

LANGUAGE
?
SYMBOL
.
 

METAPHOR
WHAT DOES IT
MEAN
DEEP
DOWN
 

ABSTRACT RELATIONSHIPS
 

MATHEMATICS
?

HOW DID HE DO THAT
?

MAGIC
o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o
 Imagine that you are wandering in these three forests of dots but can see only about as far as the average distance between dots.
"Completely ordered"

Positions of more distant dots can be accurately determined by sampling a small cluster of nearby dots

 Information content is minimal. These patterns can also represent entropy, but only at a very deep level of abstraction.

The pattern is a square array of dots extending indefinitely in two dimension.
?
How could you become able to predict where the more distant dots are located?
"Completely random"

Positions of distant dots cannot be estimated by examining nearby dots.  (There is some uniformity of density of dots.)

 Information content is maximal.

The dots are randomly placed.
?
This forest of dots has almost as much pattern as the regular array.  You can actually see the pattern...if you discover how.
"Highly ordered"
(but the order is hidden)
 The pattern is a two-dimensional space group of point groups which are squares of nine dots in a symmetrical square array. 
"Magic" trick

Cross or spread your eyes slightly to fuse any adjacent pair of those four dots across the bottom of the array.  The squares of nine are then seen stereoscopically.

The above might be seen as a metaphor for life.

We look at the world (or listen, or feel, or...) and, according to what we discover, decide how to act on that world.  We need to anticipate the outcome of our action so we can gain some kind of advantage.  It's through patterns, regularities, and constancies that we can anticipate.

(The above concept is a good place to start to understand thermodynamics and, especially, entropy.  Part of Erwin Schr?dinger's answer to the question "What is Life?" was the observation that the essence of "energy," the thing in food and fuel that is necessary for life and for the operations of our engines, is not the energy of physics but rather is the removal of unavoidable entropy buildups.  Entropy is a measure of the predictability of what a system of particles—atoms, molecules, electrons, etc—will do next. CLICK HERE to clear up your misconceptions about entropy.)
.
 It is also a  metaphor for science:
.
Knowledge starts with
PERCEPTION,

proceeds to speculation
IMAGINATION,

then to definitions of terms
METAPHOR (LANGUAGE).

Science leaves ordinary human thinking by going to the next step:
the recognition of abstract patterns, of patterns of patterns: it goes to
MATHEMATICS.
We cannot understand science until we perceive the patterns of mathematics.
Teachers love the magic.  Want to share the magic.  Teach by starting with the magic.  BIG mistake!
We cannot skip a step on the path to science.
"Pseudoscience" skips that crucial step.
Science ? Pseudoscience
Pattern Recognition        ?                            Profound Desire

"Seeing" some science concept is quite different from wishing something to be so.  No matter how much we wish for something, seeing some abstract pattern might demonstrate to us that it just isn't so. 

No matter how strong our wish for the millions of dollars in the lottery jackpot, seeing the patterns of statistics demonstrates to us that the probability of winning it is ZERO (zilch!), to eight significant figures, and the probability of losing money in the long run is ONE (certainty!), to eight significant figures.  See What's New.

No matter how strong our wish that quantum mechanics and Einstein's relativity suggest that we will someday find some way that our minds can control that roulette wheel (riches are ours!), seeing the patterns that guided Einstein and the quantum mechanickers demonstrates quite the opposite; Einstein assumed, as a starting point for his great discovery, that such mind control is absurd.   The Uncertainty Principle is actually trying to shake us by the shoulders to get our attention to tell us to look in a another direction, one we never suspected exists.  Relativity and quantum mechanics are MAGIC.

We do not jump off the top of a tall building flapping our hands, expecting to fly to the top of the building across town.  We see the world deeply enough to understand why because we need see only the PERCEPTION and the IMAGINATION levels of abstraction.  Somebody was able to design and build helicopters that can fly us from building top to building top because they mastered some of the science that takes us into the METAPHOR and MATHEMATICS levels of abstraction.

Those who see some science principle often label some idea "pseudoscience" because they see something not seen by somebody else, something that perhaps reminds them a little of watching the naive being taken in by the glittering allure of wealth dangled in front of them by the casinos and lotteries.   Pseudoscience is thinking about things that science thinks about without going deeply enough into the levels of abstraction from which science grew.

It's not "just a matter of personal opinion."  When you "see," you know that if you act on what you see you have an advantage over the person who does not see.  And if you do act on it, that person just might end up feeling that you are using some kind of magic.



Arriving at the top of the parking structure at SW First and Davis  ? no hand flapping needed

EXPLORE
feedback
fields
measure - tensor
energy
color
some suggestion for links that expand on "Perception to Magic"

RETURN TO PDX