Let me first say that as far as I can say, there is nothing supernatural about dark matter, whatever interpretation of the word "supernatural" you choose. After all, we are pretty likely to learn that it is mostly composed of the neutralinos which are as natural particles as photons (their superpartners' cousins) or electrons or neutrinos (other spin-1/2 particles).
(I avoided quarks because they are confined which could be another type of "supernatural" for some people and I don't want to add new layers of technicalities.)
There is simply nothing wrong about some matter species being badly observable by our eyes. Our eyes are not omnipotent. There's no good reason to believe that Nature has equipped us with omnipotent eyes. So we shouldn't be shocked that there are things in Nature we can't see well with our eyes. They look dark.
But that doesn't mean that they're less real. At night, most objects in our apartments are dark which doesn't mean that they're not there. ;-) Also, ordinary neutrinos are pretty dark, too. After all, they represent a part of dark matter, too.
How science would deal with the supernatural
The problematic discussion is whether science could, in principle, ever discover things that are supernatural - or admit that there are supernatural things. Well, with some more refined definition of "supernatural", science could indeed do so. In fact, it has already done so many times, as the example of quantum mechanics demonstrates.
The only thing that science will never do is to "find out" that some aspects of our observations are so confusing that they should never be studied and that nothing can be said about them. Science will never tell us that some questions about the world of observations are taboos. Defeatism is the only attitude that is incompatible with the scientific research.
Let's return to the topic discussed at Cosmic Variance. The first three types of "supernatural" are
- the silent: they don't influence the observable world in any way
- the hidden: they influence the observable world indirectly but are not directly seen
- the lawless: they influence the real world but don't obey any laws of the scientific type
Now, indeed, the silent things can simply be forgotten or ignored. They can't be seen but they don't influence us so no one cares about them. Scientific claims about them can't be empirically tested. But that's not a big problem because these claims wouldn't matter for anything else, either. In a scientific sense, "the silent" objects don't exist.
Unphysical polarizations of particles, pure gauge configurations, auxiliary fields, and all differences between mathematically equivalent theories may actually be included in this category, too. We can't ever determine the gauge in which Nature actually is. That's the whole point of gauge symmetry. ;-) Also, we can't determine whether the world follows Heisenberg's, Schrödinger's, or Feynman's picture of quantum mechanics - because their predictions are equivalent.
But we are equally incapable to say how many angels are watching us. As long as the angels remain passive, they are outside science - and outside the real world, too. ;-) Note that it doesn't matter whether we influence such angels or not.
"The hidden" objects are very different. They're standard parts of the observable world that is being studied by science. Whether something can be seen directly is completely irrelevant for science. After all, one of the revolutions initiated by Galileo Galilei was that he appreciated that indirect observations are just as relevant for science as the direct ones.
The telescopes were just one reincarnation of this new attitude.
Once he had observed Jupiter's moons with his telescope, the Catholic elite discussed whether the observations by the telescope could be trusted. They ultimately concluded that they should have been trusted, indeed. Some people who live in 2010 are vastly more unreasonable than the Catholic Church in Galileo's times if they want to dismiss if not prohibit indirect observations in science.
Indirect observations don't have to be "less certain" or "less accurate". In fact, the most accurate and most certain observations we know of are indirect. The word "indirect" means that a transformation has to be done to determine "what is there" from "what we see". As science was getting more advanced, its observations were getting increasingly indirect and the tools used to make the observations were increasingly different from our senses.
The ATLAS and CMS detectors replace our eyes as they look inside the protons and other particles that can be produced from their energy. They look and work differently than our eyes or ears or noses or jaws or skin. The detectors also work differently than our sixth sense, the extrasensory perception, because the latter doesn't work at all. ;-)
The profound misunderstanding of this whole inevitable dynamics of science - that makes observations increasingly indirect and that makes the chain of reasoning connecting observations and theories longer than ever before (this is a sign of progress!) - is one of the main building blocks of the anti-scientific movement among creationists as well as the crackpots from the Smolin/Woit/Horgan camp.
So supernaturalness has nothing to do with the observations' being "indirect" which is a standard daily job of science and scientists.
Most of the real controversy is therefore hiding in the third type of "supernatural" things, the lawless ones. If you haven't understood it yet, that's why Lucy Lawless' image was chosen to represent this article. :-)
Well, Ms Lawless is surely involved in lots of dark matters, e.g. painting climate realists as sociopaths. But it doesn't imply that dark matter is lawless. :-)
Clearly, any kind of divine power was meant to be "lawless" in this sense. We won't be able to predict what it does and it can hide, reveal, or change its mood or rules regardless of our expectations at any moment. Feynman used to say that God is whatever we didn't understand yet: whenever we learned something new about science, the room for God shrank.
But imagine that there are things in the world that are lawless - things that don't obey deterministic laws. What would science do with them?
Well, this is no hypothetical question. Such things were found in the 1920s - electrons and atoms. Actually, all objects in the world were proved not to obey deterministic laws. And indeed, many scientists including Albert Einstein were stunned. The world became lawless according to their definition of "lawless". The new theory was incompatible with their understanding of "science".
The correct approach that scientists took was to be open-minded about the amount of "lawlessness" that Nature had. The world could have been deterministic as well as non-deterministic in the classical sense. The latter answer turned out to be correct and the physicists realized that all systems in the Universe only follow the probabilistic laws of quantum mechanics. But they're damn interesting, they fully replace the classical laws, and in many situations, the quantum predictions are much more accurate than any classical predictions could ever be.
So the lawlessness only meant that the right laws that were waiting to be found simply had a different character than the approximate Newtonian laws that had been used previously. And that's indeed the general attitude of science: science can never say "give it up".
You know, God can always tell you stop looking for the Higgs boson and then we'll talk. But science can never tell you that. So for a scientist, "supernatural" is always just a different word for "so far unknown natural". Even if an entity works according to some principles that look "lawless" to us, it's a task for a scientist to find more details about this "lawlessness".
In the case of quantum mechanics, people had to find the probabilistic distributions that governed the "random outcomes" of the experiments with the small particles. That's because the word "random" is too vague; the next step is always to ask about the distribution. And indeed, the whole science was reinterpreted in this way. The goal of the most general theory of Nature is to predict the probabilities of different outcomes of a measurement.
Once again, the scientist's attitude is that the word "supernatural" can only be a zeroth approximation of the true answer. A scientist will continue to study the "supernatural" object or entity and he or she will get more familiar with it. When he or she gets sufficiently familiar, the system will look sufficiently ordinary and science may also call it "natural" just like others.
Some aspects of our observations could resist our attempts to understand them. But in that case they would be just "confusing" rather than "supernatural". And many things that have been confusing in the past were later understood. In science, "confusing" is a temporary state of affairs. To say the least, as long as science is alive, the scientist will never accept that a question has to be "eternally confusing".
So if we lived in a world where evidence would make it extremely likely that God has manually created the species one by one, there would be lots of extra questions about the timing and location of the creation procedures and the priorities that the Creator wanted to maximize, and so on. At the end, a scientist would de facto become an assistant to Mr God. The scientist would know pretty much everything about Mr God's production of the animals - and the scientist could replace God in His job, too. Apologies to religious readers who find this analogy blasphemous. :-)
We just happen to live in a world where the laws of physics work somewhat differently, I think.
(The only world where the procedure of learning explained above could fail would be a world where you should know that you should not try to learn and know important things about the world - and remain an obedient ignorant sheep. But such a world is logically inconsistent because the very insight that "you shouldn't know things" is important and as a consequence, you shouldn't know it, either.)
To summarize, the real difference is not between "natural" and "supernatural" but between the "desire to learn how things work" and the "defeatism and self-humiliation while facing the unknown". The first attitude is closer to science while the latter is closer to religion.
Sean Carroll and many commenters have written pretty much the same thing as your humble correspondent. Moshe Rozali apparently doesn't like this answer because, as he points out, science depends on the separation of the observations into "repeatable phenomena" and "contingent facts". The boundary between the two groups is "time-dependent, culture-dependent, and theory-dependent".
Well, indeed. But I would change some words and reorganize the three adjectives which will clarify them a little bit more rationally. First, it is not "science itself" that depends on the boundary but only specific scientific hypotheses do. The boundary between "repeatable phenomena" and "contingent facts" is theory-dependent - and theories that exist depend on the time and culture (which is irrelevant from a scientific vantage point). The boundary is a part of the conjectures that are being compared with the competing hypotheses, too.
(The xerographic distribution is a part of the hypotheses that have to be tested and that may be falsified, too.)
Obviously, a powerful explanatory theory tries to put as many observations into the "repeatable phenomena" group because such a theory becomes more predictive and therefore more convincing.
In this context, I have to explain that being "predictive" is not just some additional dogma one should insert into the scientific process. Quite on the contrary: one can show that being more "predictive" in this sense means that the theory is more likely than the "less predictive" theories. Why?
If theory "A" predicts the results of experiments "C,D,E" and theory "B" says that they're random, then the observations that confirm the "C,D,E" prediction of "A" increase the odds of "A" more than they increase the odds of "B". That's a simple consequence of Bayesian inference. The theory "B" predicted that 1 random outcome "C,D,E" among "N" possible outcomes will take place.
So the probability that, assuming that "B" is valid, it is exactly "C,D,E" that is observed is just "1/N" (or you can take a non-uniform measure for the possibilities, but I want to convey a general idea, so let me not go into it). The probability of "B" itself therefore has to be divided by "N", too. That's what Bayes' formula dictates. Meanwhile, the probability of "A" is not changed in this step of logical inference because the probability that "C,D,E" occurs assuming "A" was 100%.
This process will support more predictive theories over time and disfavor the less predictive ones. If your alternative theory of the Solar System claims that the position of Jupiter is "lawless", the probability that your alternative theory is valid will get a severe "relative" blow every time Jupiter is observed and found to agree with the conventional theories of gravity.
The only reason why we don't have too many theories with many more facts included into the "repeatable phenomena" group and many fewer facts counted as "random contingencies" is that all theories that would explain things with (almost) no "random contingencies" have already been ruled out.
But if you invent e.g. a theory that will be able to revive Kepler's ideas that the planetary orbital radii are linked to the sides of Platonic polyhedra, good for you. If your hypothesis will be compatible with the other - directly or indirectly - observed facts about gravity and the birth of the Solar System, you will surely become very famous.
Meanwhile, the radii of the planetary orbits seem to be "random contingencies" - which is, much like the word "supernatural", just a placeholder that labels facts whose "inner wisdom doesn't make any sense to us at this moment". However, the amount of "sense" that these data make to us can change in the future. I bet it will never "radically" change in the future and many things that seem "manifestly" random and contingent will remain so. But there's no "complete proof".
Science is making progress at many levels. For example, chaos theory "explains" where the asteroid belt (between Mars and Jupiter) can be located and where it cannot be located. These otherwise "contingent" facts are not completely unconstrained. It's just not true that nothing can be learned about them.
On the other hand, we actually have a complete proof that the probabilistic character of quantum mechanics is real and cannot result from hidden variables that follow deterministic rules.
There are things in science that are already understood and settled; and others that are not. As science is making progress, it is usually moving questions from the second group to the first group. The more science knows, the more insufficient and inaccurate the terms similar to "supernatural" will become. A scientist simply wants to know more about an arbitrarily shocking, surprising, or dark object or phenomenon. And the more familiar with them he becomes, the more inclined he will be to call them "natural".
And that's the memo.