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The laws of science can be tough nuts to crack. It can be years before some of understand what it means that the square of the orbital period of any planet is proportional to the cube of the semimajor axis of its orbit, as Kepler's Third decrees. Thankfully, they aren't all like that. For example, Clarke's Laws of Prediction are much more understandable - and catchy. Of course, since Arthur C. Clarke, who was a science fiction writer in addition to being a scientist, was able to place aesthetics ahead of scientific rigor, this isn't exactly surprising. They are not a description of some natural process, but a commentary on the scientific process.
1.
When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is almost certainly wrong.
Right away, Clarke shows that these laws can't be taken too seriously-anyone can see that all it would take to disprove this law would be some antiquated physicist saying that a perpetual motion machine is possible. Rather, Clarke is trying to impart an infinite optimism about the potential of mankind. As a science fiction writer, this is what he did for a living. To quote the man, "I believe one should be optimistic because there is a chance of a good self-fulfilling prophecy."
2.
The only way of discovering the limits of the possible is to venture a little way past them into the impossible.
Again, Clarke isn't focusing on the veracity of his law - this time leaving a logical paradox - but on the confidence in the possibilities of science. It is interesting to note that, before his debut as a writer, Clarke dabbled in actual hard science; by "dabbled" I mean "created a plan for a geosynchronous orbit for communications satellites that are essential to satellite TV and weather imaging". The next time you flip on the Discovery Channel or SyFy Network, thank Arthur C. Clarke.
3.
Any sufficiently advanced technology is indistinguishable from magic.
I don't feel like it's necessary to point out the paradox inherent in referencing magic in a supposed law of science; besides, we've already realized that it's about the spirit of the statement.
Clarke's Laws are not your typical laws of science. They don't explain some incredible feature of the natural world; instead, their focus is on the scientific process itself. Their goal is not to explain the universe, but to stimulate the desire to do so. For that, they are just as important as any traditional laws, and Arthur C. Clarke as important as any scientist. For without the aspiration to maintain and further science, those traditional laws would still be unknown.
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Image Credit: Diliff (Wikipedia)