Science succeeds by recognizing two conflicting quirks of human thinking:
| 1
A tendency to oversimplify in the service of confirming wondrous wishes
2 Discovery of abstract patterns of Nature that cannot be denied |
vs She who must be obeyed |
Both quirks are manifestations of Keith Devlin's "patterns at a fourth level of abstraction."
HUMAN PERCEPTIONS . . . HUMAN
WISHES . . . HUMAN WORDS . . . HUMAN CONCEPTS
a
shadow of the world brought to us by evolution
| 1950's | Jean Piaget asked
what specific human skills evolution developed that let us comprehend the
world the way we (sometimes)
do, especially those skills which lead to science and mathematics
...and how
it managed that task.
|
Human information functions are biological. |
| 2000 | Keith Devlin
points to four distinct levels of abstraction that represent levels of
increasing sophistication of human recognition of patterns in the world,
...patterns
that lead us to ever more effective interactions with that world.
|
Perception
Imagination Metaphor (language) Mathematics Magic
|
| 1970's | Richard Feynman
became "a volcano" (according to his wife)
as he read through the seventeen shelf-feet of K-12 science textbooks he
reviewed for the California State Curriculum Commission, all
of
which
... were written
by people "who don't know what the hell they are talking about."
|
Elementary science comes
out of evolution's human brain--capable of abstraction leading to more
and more complete grasp of the world's patterns (to
let man avoid Mother Nature's traps)
...but
even the "experts" who wrote those texts only rarely got it right
|
The scientist who
uses science sees the concepts at the fourth level of abstraction.
Teachers and learners
who do not use the science almost always work in the third level.
"He
who can does; he who cannot teaches."
...GBS
|
|
Or learning of facts. It's seeing certain abstract relationships Seeing patterns that exist much deeper than our perceptions. Science is simple, but seldom seen. Science is simple but subtle. Mathematics, too, is something very different from what it's usually thought to be. |
|
What is the "fourth level"?
| The Boolean relationship
of implication is an example of a fourth-level abstraction.
See it seen, and see it missed:
|
The above exploration
of misunderstood elementary logic
started with the
problems of medical quackery. Pseudoscience
has very broad consequences.
It can affect us all.
Disastrously!
| Can we identify those arguments that are stuffed
with oversimplification in the service of confirming wonderful wishes?
Can we identify logical imperatives being missed by arguments which are
blind to that logic? Can we demonstrate the correctness of our identifications?
Our Web sites have pages that explore these issues. A few of those pages look at some of the broader consequences. |
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Fourth-level abstractions,
when discovered,
|