Some growth of mathematical thinking — from infancy to sciencesee
....................Same
size/colors of blocks; different sources of color
......`*'~`* '* .....Fabric colors ......Flower colors ......Paint colors 4D Our eyes tell us they are all alike. Our spectroscope tells us they are
different.

We have discovered
We have discovered
We have discovered
We have discovered
We might just let
the professional
(and perhaps learn a little of their art). But we can all open
our eyes
these abstract realities around us, and use them to help
us

The dichotomy has only two possible values and looks like this: 
US  THEM 

And next... 
vegetable mineral 

The nonparametric rank order has no "between" values and looks like: 


Proportional ordering can have any of the numerical values and looks like: 
X 

The vector has components and looks like this (in the source code of the page you are looking at) : 


The tensor has components in more than one dimension and looks like this: 

The curvature of
a sphere is just a number.
But the curvature
of a ellipsoid represents a tensor.
It depends on where—at
what point—on the surface,
and it depends on
which direction at that point.
Physicists
always have a habit of taking the simplest example of any phenomenon and
calling it "physics," leaving the more complicated examples to become the
concern of other fields... Since most of you are not going to become
physicists, but are going to go into the real world...sooner
or later you will need to use tensors.
Richard
Feynman, in The Feynman Lecture on Physics
Vol II, p 311 When Feynman's insight is seen by many people, human society will discover new paths out of many serious problems. 
Measurement
from infanthood to sciencehood
is a long, beautiful journey
Bon voyage!