The reason why this is can be explained quite elegantly by the 'opponent processing theory' of colour vision.  The problem is that this theory isn’t all that approachable, and if you do understand the gist of it, the information can be hard to recall when you actually need it.  There are lots of great articles and websites devoted to the details of the opponent processing theory, and this isn't one of them.  If you're like me, and you're simply looking for a fresh perspective on it, and maybe a simpler way to understand it’s core principles, than please keep reading.  A basic understanding of this theory will help you find the answer to numerous quirky questions regarding colour vision, like why can’t humans see the colour blueish-yellow? Or why is it when you mix green and red light you get yellow light, which seems to bear no resemblance to either of its ingredients? (Contrast this to violet, where it is fairly obvious that red and blue are being mixed). The opponent processing theory can answer them all.

To kick things off, here is a very brief overview of how the eye and brain work together to transform the light that enters our eye into the psychological perception of colour:

The light that humans can see, termed the visible specturm is made up of light of numerous wavelengths, ranging from 400nm-700nm.  There are various receptors embedded in the back of our eyes that get activated to various levels of excitement depending on the wavelength of light that is entering the eye.  These receptors are termed cones, and they can be divided into three different types (S, M, and L cones). The cones are in-turn connected to the ganglion cell, and its up to the ganglion cell to weigh the differing signal intensities it receives from each type of cone against one another (L cone vs M cone, L plus M cone vs S cone), and to then tell the brain what colour should be applied to this light in question.  

That may very well be the briefest explanation of the opponent processing theory you will ever read, and likely most confusing.  A key though to understanding how this all works is to realize that the rules for what colour our brain is going to perceive for any given wavelength of light are already pre-programmed into the ganglion cell, and it's up to the cones to influence and sway this system based on how vigorous they are each reacting.   Instead of the abstract (a microscopic ganglion cell being influenced by varying degrees of electrochemical impulses generated by different cones), imagine a pulley a system whose equilibrium is affected by varying weights being dropped at different locations via different receptors.  To take this idea further, lets create a physical model to help clarify.  To do this, I have created a Rube Goldberg type of machine, and for it to be extra memorable, its made of Lego.  Let's call it the Lego Colour Vision Contraption.


The Lego Colour Vision Contraption is composed of Lego cone receptors, a Lego ganglion cell pulley system, and a Lego visual cortex.  When all the vats of paint are the same weight, the system is in equilibrium, and no paint will spill.

In our Lego Colour Vision Contraption, the Lego cones are resting on three shelves, with each shelf positioned above a different platform on the Lego ganglion cell pulley system.  On each shelf is an antenna to receive the signal, and various stacks of Lego blocks of differing heights. It is these stacks that will represent how ‘excited’ the cone is based on the light it is detecting.  If it is very excited, the cone will release via a trapdoor the tallest (and therefore heaviest) Lego stack onto the awaiting ganglion cell platform situated directly below it. If the cone is only mildly excited, it will discharge a shorter (and lighter) stack.  It is the differing weights of these stacks that will cause the ganglion cell pulley system to fallout of equilibrium and begin spilling paint.


The Lego L-cone and M-cone.  The various stacks of Lego weights are awaiting to be discharged, and dropped down to the ganglion cell platform awaiting below.  The L-cone prefers light of longer wavelengths, and will drop its biggest stack if light of about 580nm is present, while the M-cone has slightly different preferences, and will get most excitied at 545nm of light.

The Lego S-cone.  Like the other two cones, the S-cone is composed of various stacks of Lego weights awaiting to be discharged onto the ganglion cell platform awaiting below.  The S-cone prefers light of shorter wavelengths, and will drop its biggest stack if light of about 430nm is present.

The Lego S-cone.  Like the other two cones, the S-cone is composed of various stacks of Lego weights awaiting to be discharged onto the ganglion cell platform awaiting below.  The S-cone prefers light of shorter wavelengths, and will drop its biggest stack if light of about 430nm is present.

An example of the M-cone being very excited by the light present, and therefore dropping its heaviest weight onto the platform of the ganglion cell's green vat.  With the green vat now being heavier than the red one, the red and green vat fallout of equilibrium as the green vat drops and the red vat rises.  This allows the green vat's spout to open, and paint to spill.

In this scenario, both the L-cone and M-cone are equally excited, and drop equal size weights onto the red and green vats respectively.  Since the red and green vats are still of equal weight, neither colour of paint can be spilled.  However, their whole side of the larger pulley system is now heavier, causing them to drop slightly and the blue vat at the other end of the pulley to lift.  This unblocks the yellow vat, and yellow paint begins to flow.  This would be the exact reaction seen if 560nm of light was present, and why humans interprut 560nm light as yellow light.

By simply knowing each cones prefererence for wavelengths, one can conceptualize how the weights will fall, how the vats will move, and which paint will get spilled.  Specifically, this is which Lego stack will drop for each cone at various wavelengths:


We can now run the whole process from start to finish to see it all in action.  Quickly look at the preferred wavelength activations for each cone above, and see if you can figure out what will happen to the vats of paint and the pulleys when 645nm of light is presented to the cones.  Once your ready, look below for the answer: 

From start to finish, we can see the light of 645nm turning on, and the L-cone becoming slightly more activated than the M-cone (the S-cone doesnt turn on at all).  Because a slightly larger weight is dropped onto the red vat than the green vat, some red paint spills.  However, since there is at least some weight on both the red and green vats, their whole side of the larger pulley drops slighlty, lifting the blue vat, and allowing some yellow paint to spill as well.  The yellow paint only stops flowing once it becomes lighter and floats upwards on its rails.  The visual cortex recieves both red and yellow paint, and combines it to orange, which is what we see 645nm light as: orange light. 

At this point, it may have become obvious why humans cannot see either reddish-green or blueish-yellow, and that is because there is no possible combination of weights that will allow both the red and green paint to spill simultaneously, nor is there a combination that lets the blue and yellow spill at the same time.  

Dr. Burke is an optometrist practicing at Calgary Vision Centre.  He spells colour with a 'u' because its the right way to spell it.  Opinions above do not constitute medical advice, and readers should consult with their optometrist if they have questions or concerns about their eye health