Genady

Hmm... Reminded me that the OP, @Commander, hasn't acknowledged my answer above to the last puzzle.

I suspect that they never had or lost pigmentation on the underside because it is not needed. Also possible, that an ancestor of rays was pelagic with a light underside like in manta rays, for example. The stingrays evolved to be bottom dwellers but retained the light underside of the ancestor.

Neither countershading nor "light against surface" explanations seem applicable to bottom dwelling animals, such as stingrays and countless others with similar dark-top-light-bottom coloration.

Yes, certainly could. Dark when viewed from above against the dark background and light when viewed from below against the light background. Like the explanation for the sharks which I've mentioned here: https://www.scienceforums.net/topic/128920-camouflage-examples/?do=findComment&comment=1243465. The same perhaps holds for the manta:

I don't see how the countershading hypothesis applies to the green turtle. I'd rather hypothesize that the top is dark for the camouflage purpose, and the belly is light because of lack of this purpose.

Russians fighting Russians. Ура!

Yes, not much, but recently indeed some supporting studies appeared. This is perhaps the latest, from 2020: Countershading enhances camouflage by reducing prey contrast - PubMed (nih.gov)

Sorry, I don't understand the question. My what?

Does this fact support this hypothesis?

Right. But repeating the same story does not make it truer. I don't say, it is not true. I just don't know of a good supporting evidence for it.

One more bit of information regarding the search and statistics, Bayesian or not: Robert Ballard, who discovered Titanic wreck, said authorities 'immediately knew' where to look when they heard the Titan's implosion, but it took days for an ROV to get there (yahoo.com) And another: 'Titanic' director James Cameron says the search for the missing sub became a 'nightmarish charade' - ABC News (go.com)

I see. Thank you. Such input is a significant factor. However, it is not a Bayesian update. The latter would've been an update based on intermediate results of an ongoing search, i.e., the step 6 in Bayesian search theory - Wikipedia:

@StringJunky, the article that I've linked in the previous comment, contains an answer to your earlier question:

Sorry, I don't remember the details of how it supposed to work. Perhaps, the white underbelly is just a lack of coloration, while the dark top / melatonin has a function... I'm not sure.

I think that rather than Bayesian Search Theory, this information was more helpful: Titanic director James Cameron accuses OceanGate of cutting corners - BBC News

There are several alternative hypothetical explanations for the light belly / dark top coloration, for example, thermal regulation and UV protection. I remember reading about a study that tried to test the counter-shading hypothesis "by the book": Assuming this hypothesis is correct, they made a prediction about how sharp the difference between the belly and the top should be in different environments, and they analyzed available data in this respect. The data seemed to support the hypothesis but was not yet statistically significant. They needed more data.

Yes, 8-10 hours round trip. E.g., Titanic tourist submersible goes missing with search under way - BBC News

We understand why no state exists with definite position and definite momentum. It is shown via basic calculus.

I don't see anything wrong with his post. You said, "I really don't think that I use heuristics." He replied, "You certainly use them." I don't understand what attitude it is an example of or what is there against yourself.

But I did not ask about any point of view on evolution. I ask a question related to scientific method. Given a hypothesis, "animals have counter shading because it balances their light reflection and makes them less visible," what test or tests could support or refute this hypothesis?

It is not about discovery, but about possible states of a particle: If a particle state has a definite position, then its momentum is a superposition of different momentum states. If a particle state has a definite momentum, then its position is a superposition of different position states. If it is in superposition of both position states and momentum states, then these mixes have to have certain spreads. Both position and momentum are not simultaneously discoverable, because there does not exist such a state where they both are definite, i.e., not superpositions.

I understand this explanation. What I am asking is, how can we know that this is WHY they have it. Maybe there is another reason? Maybe there are several different reasons? We know why engineers use this counter shading; we can just ask them. But how do we know, why this feature evolved in animals? BTW, the textbook explanation for sharks, for example, is somewhat different from yours. They say, that when other fish look at the shark from below, the shark is less visible because they see shark's light belly on the light surface background. When they look at the shark from above, the shark is less visible because they see shark's dark top on the dark bottom background.

That is what I thought, too. But it turns out to be wrong: How does the missing Titan submersible work? Here's a look inside (usatoday.com)

The uncertainty principle does not just say, "You can't go there." The uncertainty principle is not a first principle, not a given, but rather a theorem, a mathematical consequence derived from QM concepts of states and operators.

The second link, I don't trust. It is too simplified, for kids. The first link, I didn't see there anything about "more than 50-60% of vertabrates species are .........Except primates & a lot of birds....they mainly can see colors......" In fact, many years ago I studied biology, and got Master Degree (M.Sc.) in biology. One of my favorite courses was Animal Behavior, which I passed with A+. I remember well from that course that most, almost all animals have color vision. Usually, it is different from us, but they do have it. Some see fewer colors than us, some see more colors than us, most see different color than us. Regarding the first question, how one can support your explanation of why some animals have white/light belly? You didn't give any answer to it.