"Science has no interest at all in, or ability to study anything beyond the natural."
Science doesn't like being anthropomorphized.
I mean that only partially in jest. You mean "science" here as shorthand for "people who follow the natural philosophy known as 'science'". I'll call those people 'scientists', as is the normal practice.
The thing is, there are scientists who investigate putative supernatural events, such as ESP in its various forms, or supernatural events like stigmata from a stone sculpture.
This is possible because some supernatural events affect the natural world. If someone says they can use dowsing to detect a buried bottle of water, then the success is part of the natural world. If during unblinded tests they can find the water while during blinded tests they cannot, then it's likely that any success is not due to a supernatural agent but to to the internal knowledge of the dowser.
Similarly, some claim that water molecules can be influenced by thought. (Eg, the film 'What the Bleep Do We Know'.) Such claims can be tested, which puts them in the natural world.
However, other supernatural events, such as received wisdom, might have no impact on the natural world. If you say the god Mxyzptlk told you that left-handed people should not eat soup, then there's nothing that science can do or say about it.
While if you say that Mxyzptlk told you that William the Conqueror in 1072 liked to smoke Cuban cigars and eat macadamia nuts while watching Game of Thrones, then science still can't say if Mxyzptlk does or doesn't exist, but can show that such an event was ahistorical. It is much more likely that Mxyzptlk doesn't exist, or that Mxyzptlk told you a lie.
Going back to your phrase "Science has no interest at all in, or ability to study anything beyond the natural". What you say is true. If something has no impact on the natural word, then there's nothing that science can do or say about it. But the vast majority of supernatural event also have a natural component, and those real-world effects are in the domain of science.
Are you limiting yourself to only those events with no real-world effect? Or do you want to include supernatural events like a global flooding, which would leave physical traces had it occurred?
Science is only applicable to physical phenomena with physical causes due to consistent natural law; "supernatural" is a term for things that don't meet that description. At most -- e.g., for physical phenomena with nonphysical causes, or causes that are not governed by consistent natural law -- a scientific approach to supernatural will simply identify gaps in the ability to construct a scientific model no different than if the governing natural law were not correctly identified out the physical causes were outside our current ability to detect.
The issue is not the interest of scientist, is the applicability and function of the method known as "science".
Global flooding isn't inherently a supernatural event, and can be investigated with science, but science cannot, by its very nature, address any supernatural cause, ask it can do is produce a natural model of causation.
Let us suppose that it is possible to "petition the Lord with prayer", to quote Morrison. For example, do prayers from strangers help someone recover from an illness?
We can test two populations, ones who receive stranger prayer, and ones who do not, and see if one population gets better treatment. We can look at the epidemiology to see if people from one religion, who practice healing prayer, have different health outcomes than those who do not. (This is tricky but not intractable because there is more than one factor at play.)
Thus we have the ability to detect if there is something outside of the current model. Detecting failures of the current model is part of science, even when it it cannot produce a better model other than "here there be dragons." What's at issue is that so far those gaps seem to get smaller and smaller the more we look into them. Hence the phrase "God of the gaps."
We of course have many examples of thing which were outside of the then-current understanding of science. The "ultraviolet catastrophe" is a classic example. The irreconcilability of general relativity and quantum mechanics is another.
But we did not call that "supernatural", even though when we knew there was a gap in our understanding.
At this point, global flooding of the sort discussed would have to be a supernatural event. There is no place for the water to come from or go to. There is no physical trace of such an event. Therefore, it would either require planetary engineering of the sort more appropriate for science fiction, or some sort of magical or divine intervention.
> Let us suppose that it is possible to "petition the Lord with prayer", to quote Morrison.
That's obviously possible.
What's subject to debate is whether that action in the material universe produces any change in outcomes in the material universe.
> We can test two populations, ones who receive stranger prayer, and ones who do not, and see if one population gets better treatment. We can look at the epidemiology to see if people from one religion, who practice healing prayer, have different health outcomes than those who do not. (This is tricky but not intractable because there is more than one factor at play.)
Sure.
> Thus we have the ability to detect if there is something outside of the current model.
Science is all about detecting things outside the current model, creating a hypothetical models which include those things, validating whether they explain observed realities better than the current model, and updating models.
OTOH, once it does so, the new model is still, by definition, a naturalistic model which excludes the supernatural. If intercessory prayer has an influence on health effects, not only can science detect it -- but by detecting it can quantify it (even if the necessary model is one of changes in the probability distribution of outcomes, not a simple direct consistent change in outcomes) and incorporate it into a naturalistic model.
> At this point, global flooding of the sort discussed would have to be a supernatural event. There is no place for the water to come from or go to.
No, it wouldn't. The lack of knowledge of the details of the mechanism or explanation for something which is nevertheless an element of the best model does not suddenly make the incompletely-explained thing supernatural; otherwise, things like the Planck constant are "supernatural".
That has to be mostly in jest, right? Science has nothing at all to do with the fantasies you describe. However, scientists may study the human mind, and try to describe why it clings to irrational flights of fancy like that. So if the human mind is considered to be separate from nature, then there's a concrete example of scientists studying something 'not in nature'.
However, other supernatural events, such as received wisdom, might have no impact on the natural world. If you say the god Mxyzptlk told you that left-handed people should not eat soup, then there's nothing that science can do or say about it.
Neuroscience may have something to say about the origin within one's brain of the idea that Mxyzptlk has any opinion whatsoever about left-handed soup eaters.
Science doesn't like being anthropomorphized.
I mean that only partially in jest. You mean "science" here as shorthand for "people who follow the natural philosophy known as 'science'". I'll call those people 'scientists', as is the normal practice.
The thing is, there are scientists who investigate putative supernatural events, such as ESP in its various forms, or supernatural events like stigmata from a stone sculpture.
This is possible because some supernatural events affect the natural world. If someone says they can use dowsing to detect a buried bottle of water, then the success is part of the natural world. If during unblinded tests they can find the water while during blinded tests they cannot, then it's likely that any success is not due to a supernatural agent but to to the internal knowledge of the dowser.
Similarly, some claim that water molecules can be influenced by thought. (Eg, the film 'What the Bleep Do We Know'.) Such claims can be tested, which puts them in the natural world.
However, other supernatural events, such as received wisdom, might have no impact on the natural world. If you say the god Mxyzptlk told you that left-handed people should not eat soup, then there's nothing that science can do or say about it.
While if you say that Mxyzptlk told you that William the Conqueror in 1072 liked to smoke Cuban cigars and eat macadamia nuts while watching Game of Thrones, then science still can't say if Mxyzptlk does or doesn't exist, but can show that such an event was ahistorical. It is much more likely that Mxyzptlk doesn't exist, or that Mxyzptlk told you a lie.
Going back to your phrase "Science has no interest at all in, or ability to study anything beyond the natural". What you say is true. If something has no impact on the natural word, then there's nothing that science can do or say about it. But the vast majority of supernatural event also have a natural component, and those real-world effects are in the domain of science.
Are you limiting yourself to only those events with no real-world effect? Or do you want to include supernatural events like a global flooding, which would leave physical traces had it occurred?