Science is an exacting, meticulous process of continuously discovering that most of what we think we know about the universe is wrong, discarding it, and replacing it with something incrementally closer to the truth as measured by how much of the universe it manages to successfully and self-consistently explain.
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Re: (part 1)
(Well, actually, I should qualify that. No exception to Newton's laws has been shown, in the Newtonian frame. Einstein and Lorentz, among others, showed that Newton's laws do not apply, unmodified, in other frames of reference. The laws of thermodynamics have still proven unassailable to date, in any reference frame; most recently, even black holes have been found to obey thermodynamics, in that it has been shown that they do not in fact destroy information about what they consume.)
Your example of multiplying Roman numerals does not strike me as the counter-example you appear to think it is. In the first place, "Things everyone knows" and "Laws of science|mathematics" are not the same thing. Everyone "knew" that heavier-than-air machines could not fly, until the Wright Brothers did it. In the 1700s, it was common "knowledge" that the human body could not long survive the terrible stresses of speeds in excess of twenty-five miles per hour. And from Greco-Roman times until the Renaissance, everyone "knew" that there were only four elements — earth, air, fire, and water. But hah! Becher proved that old canard false in 1667, when he discovered phlogiston.
In the second place, is the crucial fact here that he was the first since perhaps mediaeval times to say "This doesn't make sense, the Romans couldn't have done what they did without multiplication and division", or was he simply the first person since people started saying that to not only say it, but also have both the necessary mathematical tools at his disposal and the key insight that enabled him to rediscover how to do it?
Re: (part 1)
I brought up the example to point out that starting out from the point that your mental perception is "well that can't be done" is a self-fulfilling prophecy.
Do I think Newton's Laws will "be broken"? Not by anyone who perceives them as laws. Do I believe they are what's the word you used "unassailable"? No. My own life-experience has shown me otherwise... it's a locked entry, but I'll link it for you so you know part of why I'm saying what I am http://yndy.livejournal.com/610339.html
The whole point of what I am replying with is that one's ontology forms not just one's perceptions of the universe, but one's ability to perceive differently.
Examining the language is crucial.
Law (http://dictionary.reference.com/browse/law)
"invariable" and "rule" are both inflexible terms.
Here's a different example that may illustrate what I'm trying to point out to you about your ontological map of the universe. Go look up the verb "sex" in any dictionary. Usually you'll get rerouted to sexual intercourse or coitus... despite the fact that recent years have seen a movement toward non-gender specific sex, the entries still show "esp. between a man and a woman" or "esp. inserting penis into a vagina". For literally decades (centuries?) anything that didn't include one of each gender was not defined as sex. So what exactly were gay men and lesbians engaging in?
How we as a society perceive words (no, not the individual 'well I define it thusly even tho that's not it's accepted definition' argument) limits us in how we perceive the universe - and also limits us into areas of inquiry.
"But why would we doubt that? No one has ever found a way around it...yet"