Science is seeing
in more and more sophisticated ways.
But...

SEEING
IS
A MATTER OF LOOKING
IN THE NEEDED WAYS
 BUT UNTIL WE
DEVELOP THE NEEDED
PERCEPTION, WE WILL
NOT "SEE."
The science we must "see" in order to understand the differences in human color vision is simple, but it is quite subtle.  It involves understandings that were "seen" by no one earlier than a few centuries ago.

The most important difference between normal and protanopic color is a kind of mathematical dimensionality.  You can see that difference—or at least a consequence of the difference—with a strong magnifying lens.  Look at the dots on your computer screen in those two photographs.  You see three kinds of dots:  blue dots, green dots and red dots.  All three are used in the "Normal" photo.  The red dots are turned off in the "Protanopic" photo.
 


Normal

Protanopic 
You see three different colors of dots on your screen because we have three different kinds of cones in our eyes.  The three phosphors on your screen come fairly close to matching the sensitivities of the three kinds of cones in the normal human eye.  The red phosphor is not needed for images seen by eyes that don't have the red-sensitive cones.  Look at the right-most green panel at the top of the page with your magnifying lens.  You will see a few red dots turned on.  They show the letters of  the message.
(The trick of turning off the red dots on the screen doesn't quite show a color "normal" person what a protanope sees, and a protanope does see the messages depicted as orange on a green background, but not remotely as well as "normal" vision sees them—but the trick's a good approximation.)
Navigating Second Glances
Seeing further

footnote:
Dimensionality ofcolor

The "dimensionality" of color vision is the dimensionality of the space needed to organize all the colors that the vision can discriminate between.  (For really understanding what this means, you can't beat actually trying to organize a big bunch of paint samples.)  If we had four different kinds of cones, it would take four dimensions, and it would take four different colors of dots on our computer monitors, backed up with four channels of color information processing.  The maximum possible color dimensions is infinity, which is the dimensionality of spectrographic color.

All colors that we can see, except the pure spectral colors, can be made with mixtures of pure colors, and there are an infinite number of different mixtures that will produce the same color as seen by normal human color vision.  Our vision is "blind" to those differences.  A spectroscope can distinguish all of them.

The mathematics that lets us ask and answer questions about such "color spaces" came out of the science of the last part of the 19th century.  We "see" far beyond human color through this mathematics, but it's an empowerment that requires that we develop human thinking skills unknown before the last several centuries.  Watch this Web site for "Hilbert's Prism," coming soon.

These skills somewhat resemble the "insight" of stereopsis in the ways they seem to form, in the "obviousness" of what we "see," in the resistance to—even impossibility of—simple "learning," in the lack of meaning of "unlearning,"  and in the fact that some people acquire the skills past what might seem to be a "critical age."

Colorblindness does not seem to be "correctable" at any age.  Stereopsis blindness has been corrected at ages a few years past the critical age of 10-19 weeks.  Any critical age for the most advanced skills seems to be a different phenomenon than the critical age for, say stereopsis and language. However, if we want to become able to "see," we have to resist the allure of anti-intellectualism and the ease of letting others do the hard work of thinking deeply for us.  Today, large numbers of physics students are "seeing" physics that in the past only a "gifted" few managed to master—and they do it through hard mental effort.  There may well be hope at any age.  Learn a bit about this research by going to the Web site of the U. of Wash. Physics Department.  It's linked ("recent research") from this site at the "Seek Eurekas" section you can get to via the Back Door.