Visualize it!
Good mathematicians do it a lot.
Theoretical physicists often make a point of it.
.

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

Once upon a time...
we were all infants...
 looking

...seeing
...but human infants.

So we tried to make sense of the world around us. We discovered we could sort things...
bigger - smaller

Sorting into piles
either/or
We can do better!
There's more than "either/or."
!
Look! We can line 'em up.
Ordering by size
An make it look nice.
Proportional ordering   --   Ratio
Let's do something with it!
Let's

PUT PEOPLE IN THEIR PLACE.

Some people are
"brighter" than others.
1-D
Hey!  Something's wrong there.
People are
sometimes "brighter"
in different ways.

2-D
It's still wrong!
 There's more than "either/or."
!
There are more than two ways.
3-D
There's ultraviolet.
There are more differences 
than we can see
!
There's infrared.
....................Same size/colors of blocks; different sources of color
......`*'~`* '* 
.....Fabric colors 
......Flower colors 
......Paint colors 4-D
Our eyes tell us they are all alike.  Our spectroscope tells us they

are different.
Spectroscopic "color" has an infinity of dimensions.

There's x-rays, radio waves, cosmic...

We have discovered 
multi-dimensional
spaces.

We have discovered
degrees of freedom.

We have discovered
vector spaces.

We have discovered
orthogonal
basis vectors.

We might just let the professional
mathematicians do what they do
with such magical things,

(and perhaps learn a little of their art).

But we can all open our eyes
to these wondrous
discoveries,

these abstract realities around us,

and use them to help us
avoid making mistakes,
maybe tragic mistakes!
over what we don't see.

 
The dichotomy has only two possible values and looks like this:
ME  -   YOU

US   -   THEM
And next...
animal
vegetable
mineral
The non-parametric rank order has no "between" values and looks like:
*
Proportional ordering can have any of the numerical values and looks like:
Y
X
The vector has components and looks like this (in the source code of the page you are looking at) :
color = # 39 63 0D
The tensor has components in more than one dimension and looks like this:
-1
5
7
6
56
0
3
23
2i

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 31-1
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!