I've generally heard about 12 million but the point is, it's not anything like 16.7 or billions: IF you can't see it, it's not a color. So the bit (no pun intended) about such massive numbers of device values is, they are all not all colors (assuming we agree upon 12 million and marketing states billions, there's more we can't see than we can by a massive margin). Yet marketing from many, many companies keep trying to get customers to believe more is better. As for billions of device values, I'd be love anyone to demonstrate on a print that has more than 8-bits per color encoding of image data AFTER editing versus the high bit version produces any visual difference on the print. Bit depth is about editing overhead and again, I'd love to see someone demonstrate on a print, even with fine gradations that more than 8-bits per color of a final edited image is inferior to sending higher a bit cousin.
I completely agree with you in almost all respects. There was a typo in my original response where I said '1million to 14 million' - I mean to type 12 million, so apologies. Let's agree on 12 million discernible colours by a good human eye as a starting point. That is different to saying that the 4 billion theoretical combinations of R,G and B values that you can achieve using 32 bits of data re not all colours. Every single one of those combinations, fed into RGB LEDs and thus into pixels on the paper, produces a visible dot on the page. So all 4 billion combinations produce 4 billion dots. The point, as you say, is that many of those dots will look the same as each other or will not be discernible by the human eye from each other (though I'm still not convinced that the 12 million different colours you see are necessarily the same as the 12 million colours I see).
But imagine a colour whose values in some imaginary, simplified, visible RGB colour space are 1,1,1. Then imagine that the next discernible colour (varying one channel only) is 4,1,1. You and I might both agree that 2,1,1 and 3,1,1 are not discernible from 1,1,1 but they are still colours, and if I replace my two points of 1,1,1 and 4,1,1 with different points of 2,1,1 and 5,1,1 I will produce two perfectly visible (and probably discernible) dots. So one reason for having as many data points as possible is to achieve smooth gradations as you move along a tonal curve, and eliminate any stepping.
Now you are completely correct in saying that 8-bit colour is perfectly adequate in print. In fact, that's all we actually use in terms of our print engine - each of the LEDs is fed with 8-bit colour information from the RIP and that produces 16.8 million visible output combinations (some of which may still be indiscernible to the human eye). But each of our LEDs is controllable to either 11 bits or 10 bits (giving us 32bits in total). So the critical extra step that we undertake is in mapping the 24-bit data we get from an 8-bit RGB colour space to the 32-bit range of allowable inputs to our R,G and B LEDs. The thing is that silver halide paper is non-linear: a 1% increase in energy in, say, the red spectrum will typically
not produce a 1% increase in density - and the relationship between energy increase and density increase varies all the way across the range in each of the three channels. It also differs for each paper we use. So having the 2/3 extra bits in each channel allows us to make
very fine adjustments to the energy inputs of each channel at critical points in the energy curve in order to get the best possible calibration and colour profile for our printer. So, for example, about 18 months ago we were sent a test file to print by a very prominent camera manufacturer. That file consisted largely of a very pale grey sky that shaded from essentially paper-white to a very slightly darker grey, and had great subtlety throughout the mix of clouds shown. Our early attempts to print that produced a certain lack of smoothness in tonal gradation as we approached the media white point, and an inability to show all the subtlety in the clouds. We spent a good deal of time re-characterising our LED calibration in order to reproduce the correct amount of detail in those low-energy areas of the image (and we have repeated the effort at different points along the curve). I guess one of the key differentiators we would claim is that we are in a position to do this - just like (presumably) the R&D departments of any major printer manufacturer, but
unlike the average print service company that has to take the printer it has purchased in the form in which it was provided - whether or not the calibration basis is as good as it should be.
So in summary I think I would say that the point about 4 billion colours could be much better phrased. We aim to produce 16.7 million different colour values on the page (2^24 combinations from 8-bit per channel colour). But to produce these accurately and smoothly, particularly in difficult areas of the gamut, we use the extra 'detail' available from the 32 bits of input data we have available for our LEDs, which gives us 4 billion potential colour combinations. And the mapping of the 24-bit space to the 32-bit space is one of the critical steps in producing the most accurate possible printer.
