Exploring an idea
from PERCEPTION to MAGIC
Visualize it!
Good mathematicians do it a lot.
Theoretical physicists often make a point of it.
.
This is a combination of Keith Devlin's four levels of abstraction and our simple-complex / easy-difficult concept.  This chart will be used to make points about specific issues--an example of serious oversimplification from current events is given below in the blue segments.

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

<-- 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
Shape
Color
Motion
Voice quality
Temperature
My (empty) plate could be full.

Perhaps...
If I intone:
"oomm abraca..."
I can change the world.

Energy
(the capacity to do work...food)

Revenge
My rights
F = ma

Energy
(equivilant to mass)

Justice
Human rights
Civil rights
Feynman worked here. He saw things that others realized they would never have seen.
The raw material we start with.
It only seems that this is the world.  Evolution left a great deal out when developing our abilities to "see."		 We imagine things that aren't there.  Perhaps they are just memories of what had been there.  But we also can imagine what would be nice...if only... Commonalities among otherwise different things. Human beings use representations, and that leads to language.
Symbols of symbols.
Relationships that follow rules and which we can manipulate through the symbols when we can't "see" the relationships.		 Gödel is here.
Our brain's logic system cannot completely see itself.

looking...seeing
EXAMPLE
"We can do anything we like and call it self-defense"
 We must decide what we should, and what we should not, do.

Should = everything
Should not = nothing
Information 
= p1r1+ p2r2

p1= 0,  r2= 0
Information = 0
 

bigger - smaller
US - THEM

FRIEND
ENEMY

  
 

There's more than "either/or."
FRIEND
ENEMY
NEUTRALS
    
 

Ordering by size
RANK
  
 

Proportional ordering
GAME
SCORES
RATIO
PROPORTION
 
1-D
COST
SCALAR
COST/BENEFIT
.

2-D
2-VECTOR
NO
cost/benefit
.
3-D
3-VECTOR
 
i
N-VECTOR
Questions of inflicting harm on other people are at this level of complexity.
TENSOR
 If only magic can solve such problems, look out for evolution's pruning shears!

Measurement
from infanthood to sciencehood
is a long, beautiful journey

Bon voyage!