(Parenthetically, we live in an RGB world -- the cones in our foveas are sensitive either to red, green, or blue light, and both cones and moreso rods are sensitive to monochromatic brightness -- and these signals, R,G,B, and brightness are what get transmitted neurologically to our occipital cortex and constitute the data from which we perceive and interpret all visible colors).
I think that our impasse is more semantic than anything else. One has to acknowledge that the a curve and the b curve merely represent values on a linear scale. So for a given pixel, you add or subtract value from that pixel in a linear way. Thus whether you number it 0 to 255 or make 0 neutral and have it go to -127 to +127, each successive value still has the same distance from its neighbors as does every other.
As I just pointed out, this argument is built on a false assumption, that the curves are actually linear. We've been using only linear curves so far, but that has been only for pedagogical reasons. But, though all lines are cures, not all curves are lines. Consider an A curve that looks like a V with the bottom at the 0 point on the X axis. That curve will keep all the green the same but turn all the magenta into green, the more magenta a color is the more green the curve will make it. This is not a linear transformation at all and cannot be strictly described in terms of addition and subtraction.
A few pictures may be worth 1000 words here.
Take this image:
Apply this A curve:
I changed green to magenta, but made no change to the magenta of the original. QED
The mathematical ability to pull apart this relatively small data, is a strong point for Lab which cannot easily be represented in Lab, especially not in PS.
Oh, and Rutt, thanks for demonstrating so efficiently what I've been unable to make clear in words.
Is that shot from your trip to NYC this week? Perfect for the example.
Since a color cannot be both green and magenta (or blue and yellow) at the same time, LAB only has to specify how intensely green or magenta the color is. More negative values specify more intense green, 0 means no green nor magenta, and more positive values specify more magenta. Simalarly for the B channel, where more negative numbers specify more intense blue and more positive number specify more intense yellow.
The above statement is a gross oversimplification bordering on a falsehood. Our visual system is quite complex but suffice to say that the Cone cells are not sensitive either to red, green, or blue light as stated above. Each type of cell has a range of sensitivity and there is considerable overlap between the three types, e.g. the so called Red receptors for instance react to wavelengths from cyan to red with peak sensitivity to the yellow part of the spectrum.
Ironically, at least part of the information processing - done on several stages and on different locations - is in "LAB mode", following the same principles of opposing duos - light-dark, red-green and blue-yellow.