Color Science differences

You thought I'd accept it just because you say so? No chance. It seems I'll have to take you through this.
OK, the uncertainty principle says that we cannot know a both a quantum's location and its momentum to an arbitrary precision. I'm sure that you know the formula, 𝜎𝑥*𝜎𝑝 ≥ ℎ/4𝜋. 𝜎𝑥 is the standard deviation of position, 𝜎𝑝 is the standard deviation of the momentum. The momentum of a photon is 𝑝 = ℎ * 𝜆. Substitute that into the uncertainty equation and we get 𝜎𝑥*𝜎𝜆 = 1/4𝜋. So, what this means is that if we know the location of a photon to some precision (for instance, the space defined by the size of a pixel), then there is a limit to the precision with which we can know its wavelength. So, if there is a fundamental limit to the precision of measurement, there is also a limit to the the range of observations (samples) which can be differentiated. What this means is the the 'space' of observed wavelengths is not in fact infinite as you were suggesting. It is under a classical model, but not under a quantum mechanical model - which is the observable reality. It's the divergence of abstract mathematics from reality.
Not that it really matters, since as I said, more practical considerations limit the range of independent observations which we can make far more than the quantum limits do.

No, it is not. As every observation is probablistical, then probability distributions of single measurements can be imagined as intervals and like I said, there are uncountably many different subintervals on any interval of ℝ. You can't just split wavelengths from 400 to 800nm to fixed set of intervals (say 1nm wide) and say that there are now 401 of possible different resulting values.
Moreover, spectral density is statistical property of big amount of 'incoming' photons, which is not related to observer (sensor). Sure we can record different densities as identical ones, but this doesn't tell that there is only finite or even countable amount of them.

OK, I prefer your mode of discussion (to actually argue your case) to his (just make pronouncements in a kind of argumentum ad sui verecundiam). I missed your earlier reply to this. Yes, I think you're right on the statistics of it. But we've got to the point of dancing angels. The real point is that in any real case we do not need an infinite data set to describe the incoming spectral density functions, because the reality is determined by ability to actually measure something.

Deciding which colour to render each of the three columns is an 'interpretation', and amounts to 'development', albeit a very simplistic one.

I'm getting really pissed off with all this accusing me of sophistry, from you and other people. Neither of those things. The rendering you see on the screen doesn't just happen. Somewhere in the guts of your computer a piece of software decides what will be the hue of each of your 'red', 'blue' and 'green' columns, that's if you don't explicitly do it yourself by assigning RGB values. That's an 'interpretation', even if not yours. The 'method' of arranging the raw data in three columns (a very crude demosaicking) and then going through the aforementioned process of assigning RGB values is 'development'.

This I can agree. In reality we don't need any abstract math at all :)

But to discuss general concepts some kind of abstraction is needed. Like in current talk of metamerism - in light of understanding metamerism in general and possible sources of metameric failures problems with observations uncertainty or sensor technology are largely irrelevant.
Even CFA filters technology related questions are not relevant on first approximation - but to analyse reasons of real metameric failures this becomes important.

What I'm often attempting to do is to create suitable model of real system - model has to be as simple as possible and not principially wrong (this usually means that we can ignore second order or minor effects, but should not redefine first order formulas and concepts). Also I'm aware that my understanding of things may be wrong and it certainly is incomplete, thereby to discuss them I have to present my point and substantiate it - if anyone can refute it on basis of strong arguments, then I see no problem with it.

Unintentional, and I value the feedback. I don't intend to 'put people down' by simply disagreeing with them. If I stop unintentionally making people grumpy it will be a good thing. That's also why I gave feedback about me feeling grumpy. Now you know you can avoid.

LOL. The point with abstract maths is deciding which representation makes a problem more or less tractable.

The problem with the maths is that it can obscure what is a relatively simple concept, that is that you can't describe a complete spectral distribution with three scalars, so metamerism is inevitable. There will always be any number of spectral distributions that produce the same three scalars. You need the maths to actually work through a solution, but not to understand the basics of the phenomenon.

Absolutely, but mostly people here will be interested in the idea that metameric failures exist, not the detailed analysis of them.

+1 on that approach.

But if one does not understand linear algebra (or even if understands it somewhat, but not in required level), what then?

Bob's last statement "you can't describe a complete spectral distribution with three scalars, so metamerism is inevitable" is much easily understandable - it expresses the same concept, albeit not in rigorous mathematical way.

I think both views are valuable. Mathematics shows what is scientifically correct and expressing concepts in less scientifical way helps general public to not develop wrong understandings (and see problems with incorrect explanations).

How many people here are familiar with linear algebra?

That's exactly wha I didn't do. I presented my opinion and the reason it was my opinion.I don't believe that I'm always right. I just think that it's a simple courtesy if you're saying that someone's opinion is incorrect to explain why it's incorrect. You didn't have the grace even to do that. You just made a snarky comment.

I think you'll find that it does. Or it did when I did my Physics degree. That was a long time ago, maybe it has stopped since then.
Nope, it hasn't. See this from the University of Waterloo. It usefully includes instructions for experiments that show how it does. Why not have a go at them? A little bit pf practical work can be useful for a mathematician.
If you think that they got it wrong, then so did Millersville University, MIT and Harvard

Sure. If you go back along this thread you'll find that nowhere have I said that you are wrong (apart from the above comment, where you clearly are), or even suggested such a thing. I'm not sure why you're acting so hostile.