Arthur C. Clarke famously claimed:
Any sufficiently advanced technology is indistinguishable from magic.
In my eyes, this statement, while basically true, shows a misconception of what magic is—and a misconception that is shared by many others, at that.
My starting point would simply be to ask: How is magic and technology defined?
Both are somewhat vague concepts, but the definition of magic typically includes something along the lines of “paranormal”, “not explainable by science”, or similar—effectively creating a division that technology (and/or science) and magic are the natural respectively supernatural equivalents: An aeroplane is technology, because the way it flies can be explained within the realms of the natural laws; a (hypothetical) flying carpet would be magic, because it draws on the supernatural.
This, however, just obfuscates the issue: We are now left with the discussion of what is natural and supernatural (normal and paranormal, whatnot).
My take is: Magic is a phenomenon that is yet to be explained by science. In other words, the only difference between technology and magic, is that the one is something that we understand today; the other something that we do not yet understand, but eventually will.
To illustrate: Imagine that the ancient Egyptians had had some remarkable break-through in magic, somehow managing to generate artificial light by inducing magical, invisible particles to pass through fine threads of copper. The secret was lost, and as time went past this feat became considered a myth of low credibility—only believed by a minority group of supernatural experimenters, alchemists, and the like. Come the modern era, electricity, and first predecessors of the light-bulb... The minority is vindicated, magic does exist, and magicians, not electricians, become an invaluable group of professionals.
This scenario differs from reality on one single basic count: The Egyptians had no such break-through (and it would indeed have taken either an amazing feat or an extraordinary piece of good luck for it to happen).
An apparent counter-example: Science may one day be able to deliver a flying carpet; however, for one to have existed in the days of Aladdin, magic would have been needed. Not quite: There were, in fact, no flying carpets back then (and likely no Aladdin, for that matter), which makes a world of difference. A flying carpet that does not exist is, ipso facto, not magical, not flying, nor even a carpet. Assume, however, for the sake of argument that flying carpets did exist: What would make them magical? Is there any reason to expect that their flying ability would not be explainable (as opposed to “already explained”) by science? I hold that given the existence of a flying carpet there would almost certainly be a scientific explanation to be found; hypothetically, that the carpets contained cavoritew. Similarly, that science has failed to find an explanation for e.g. ESP is unremarkable and uninteresting, because there is no true indication that ESP actually exists; only if its existence can be proved, and science fails to come up with an explanation over a pro-longed period of time, can the possibility of something truly paranormal be taken into account.
Notably, much of what we today would consider primitive technology, medicine, or similar, was once considered magic by many—including such mundane things as smithing. Equally notable is that even (attempts at) magic that did not actually work has historically often been put into systems of rules that are basically scientific (by the standards of the day; not, obviously, by modern criteria), and usually followed a logical pattern (cf. e.g. http://www.gutenberg.org/dirs/etext03/bough11h.htme). Similarly, alchemy, which is usually considered either magic or related to magic today, was one of the most scientific fields that had ever existed until the modern sciences entered the field—and chemistry, a highly respectable science, is arguably a special case of alchemy (as the Christian religion is arguably a special case of the Jewish: had the Jews/Alchemist been completely swallowed by the Christians/Chemists in a comparatively short time period, there might have been very little distinction made). Similar statements apply to e.g. astrology and astronomy.
Currently, I see only one possible case of magic that could fall outside of technology/science with a non-negligible probability: Use of magic formulae, prayers, or similar, to make demons, gods, or other “magical” creatures perform acts. Even here, however, the problem would likely be more of semantics and definitions, even provided that this scenario is not hypothetical: A higher being acting in the world will likely use mechanisms explainable by science, or an extension of science to a greater or other universe; further, the actual formulae would likely be scientifically investigable and explainable. The one issue would be whether the mechanisms used by the higher beings were inherently inexplicable by the means of this world. (Such a scenario could likely be constructed in theory by assuming that this universe is run as computer simulation in another universe, and considering Gödel’s incompleteness theorems.) It is further disputable whether this should be considered magic at all (although some historical justification can be found), and not rather religion: Certainly, the current major Christian churches would react as negatively the accusation of magic, as would a chemist to the accusation of alchemy.
An important observation, that some non-scientist may be imperfectly aware of, is that even the phenomena that fall solidly into what is typically considered technology, are imperfectly explained by science, including e.g. electricity. Further, it is quite possible that trying to explain these is like plumbing a bottomless hole: It can be plumbed to a greater and greater depth, possibly even an arbitrarily large depth, but a bottom cannot be found; a “x because of y” can be amended with a “y because of z.”, “z because of z1.”, etc. but a terminal “z[high number] because.” may never be found.
A final issue: The word “magic” can be traced to the Proto-Indoeuropean root “*magh” (“to be able, have power”), which is also the root of “machine”. (Cf. http://www.etymonline.com/index.php?term=magice, respectively, http://www.etymonline.com/index.php?term=machinee.)
As I have later realized, the above is based on an implicit assumption of chains of cause and effect. This is likely not an issue—there are no signs of event A leading to event B without such a chain (at least outside advanced physics and scenarios far from “normal” life—and even there there is only speculation on the possibility).
However, this could give us definitions of magic and technology that are disjunct, sensible, and avoiding the problem of definitions at the beginning of the text.
In effect, everything occurring in the real world would be within the realm of science, but there would be a hypothetical “magic” not encompassed by it.
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