One of the problems of arguing for science with people who don't understand it or are actively hostile to it is that Science with a capital S can't promise to have all the answers. There are things science simply can't explain, real mysteries. It's not something science advocates find easy to deal with.
For one reason, some of those mysteries can be pretty esoteric. For another, scientists find it hard to discuss things they can't explain - they're supposed to know stuff after all. Doubters like to cite such things as proof of whatever reason they have for dismissing science in favor of their own pet beliefs. How is science supposed to compete against Faith with a capital F that promises all the answers anyone could ever need?
But here's the deal. Science always has things it can't explain. That's not a bug - it's a feature.
Science uses theories to put known facts into frameworks which can explain the relationships between those facts and make useful predictions as well. Generally, the better job a theory does of tying facts together, and the more accurate its predictions, the greater the validity that theory is given.
But...
More below the Orange Omnilepticon, including a link to some real mysteries of science after some discussion!
When Science and Faith square off, the results are seldom productive unless a fundamental difference between the two can be understood. True faith is supposed to be beyond questioning. It's a collection of doctrines which are held to be true in all times and all places regardless of what facts may challenge them.
Science is all about questioning - if there is no way to test if a theory is true or false, that theory can't be considered particularly useful or valid in a scientific sense. At best, it can be considered an interesting hypothesis to be put aside until some way can be found to test it.
This means even the best, most established theories have to be open to the possibility of error, of limits to the questions they can answer. You almost never have all the facts is one reason that often comes up - insufficient data in other words. Thus, generalization and extrapolation is used to bridge gaps. We do it all the time because A) it works more often than not, and B) it's awfully hard to see things that aren't there, the rare event, the unanticipated possibility, the things we haven't yet observed. Consider black swans for one.
So, the strongest theory may be shaken when confronted with a fact that it hadn't previously encountered. And that's the way it's supposed to work. Theories are judged by their ability to survive real world tests, and do it better than alternative theories. If they can't, they get replaced by something that can.
The scientific method is supposed to be a method for accumulating facts for those theories, and testing them all, one that can be done by anyone with the skills and knowledge to do so. Given the same set of facts, and the ability to evaluate them without bias, different researchers should still be able to reach the same conclusions - or agree on what further testing is needed to resolve their disagreements. And it does work that way more often than not. This is not something that can be done with faith.
(To be fair, faith is being used in a pretty absolute sense here. Faiths do tend to change over time - if not necessarily by reason and experiment. So much of what faith attempts to explain is simply not amenable to testing in an experimental sense. But science keeps pushing at those boundaries - and some faiths are more adaptable than others.)
This is something people can find hard to understand. What good is a theory if it can be disproved, compared with faith which is supposed to be above proof? And the answer is that a theory IS only as good as the evidence that supports it, the tests it can meet - but that testing has led to some pretty robust theories that have been able to stand up to every test we've been able to devise, within the limits of our abilities.
Speaking of limits, another is that a theory may only apply within a certain range of conditions. Unless you're an atomic particle, you don't normally spend your time uncertain about where you are/how fast you're moving (except for that interval between waking and consumption of that first dose of caffeine, or after that third drink.) Yet without Quantum Mechanics, the electronics we take for granted wouldn't function. If you drop a tea cup, you don't count on relativistic time dilation as it falls faster allowing you enough time to slide something soft under it to cushion the impact. But if you're sending probes between the planets, you'd better make sure your trajectory plots take it into account.
We're not always as smart as we think we are, either - in the sense that while we're constructing theories, we don't always fully understand all the aspects of the tools we're using to assemble those frameworks - until something or someone has an "Aha!" moment that changes everything. Mathematics is integral to so much of science - and yet it's a field that keeps evolving as mathematicians come up with new insights. (It may be necessary to sign up for a free limited membership to view this article at New Scientist.)
This particular example may yet fail to withstand critical review, but if it does...
Mochizuki's reasoning is alien even to other mathematicians because it probes deep philosophical questions about the foundations of mathematics, such as what we really mean by a number, says Minhyong Kim at the University of Oxford. The early 20th century saw a crisis emerge as mathematicians realised they actually had no formal way to define a number – we can talk about "three apples" or "three squares", but what exactly is the mathematical object we call "three"? No one could say.
If you'd like a less mind-boggling example, consider the difference between trying to do math problems using Roman numerals versus Arabic numbers. It's still math, but the tools affect what you can reasonably expect to accomplish, and how easily.
Which leads into another reason why science runs up against things it can't explain: conceptual limits to understanding. You can't build a framework tying facts together into a theory if you don't have the right concepts of how the pieces of that framework connect, or if you don't have a solid foundation on which to build it.
You can't really explain principles of medicine, disease, and hygiene to someone who has no concept of bacteria, viruses, etc. Semmelweis on empiric grounds founds ways to cut mortality in hospitals by rigorous hand washing - but without germ theory, he couldn't explain why it worked. Louis Pasteur was a chemist - not a physician - but his work helped lay the foundations for that theory and revolutionized medicine. It took Darwin a voyage to the Galapagos and decades of follow up work to conceive of how natural selection could lead to the myriad of different species we see around us.
And then there's a simple reason why there are mysteries science can't explain: we're up against the limits of what we know. Moving beyond those limits might require developing new concepts, accommodating new facts, rethinking our previous assumptions, all of the above, and maybe something more. It may be a case of several competing theories without enough facts to tell which one does a better job. It may be the lack of exotic/expensive hardware capable of putting a theory to a test, or just plain slogging through a lot of tedious experiments to gather enough data to make a choice.
There's a quote attributed to several individuals that "The universe is not only stranger than we imagine, it's stranger than we can imagine." (A trenchant critique I ran across a while back added "And you know what? It's even stranger than that.") The late Douglas Adams tossed off an observation in the preface to The Restaurant at the End of the Universe that:
There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.
There is another theory which states that this has already happened.
So without more ado, let me end this little piece with the reason I wrote it in the first place:
13 Things that do not make sense from
New Scientist. Yup - some real Mysteries of Science! While we're still celebrating things like the apparent discovery of the Higgs Boson or the stunning information coming back from Curiosity on Mars, it's entertaining in a maddening sort of way to realize we're still a long way from having all the answers. That's both a bug and a feature!
And if that's not enough, enjoy some classic Monty Python that gets right to the point.