The Philosophiæ Naturalis Principia Mathematica was first published in 1687, and was a work of such mastery in mathematics and physics that it was understood even by those scientists of that age as a work of phenomenal importance. It presented laws for motion and for universal gravitation, and became the foundation of all classical mechanics from that point forward. It has been supposed that, should Newton not have published it, the entire history of science would have been pushed back by centuries.
I am not here to talk about the book. It is way over my head, despite its having been written a dozen generations ago - and don't kid yourself, it is probably over your head also. I understand the basic principles, the same principles most everyone understands: that actions call for reactions, that objects display properties of inertia, that energy in a state of continuous dispersement, and that objects move in accordance with these laws as they are also effected by the mutual forces of gravitation.
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| The most important book you will never read. |
What makes all this 'Astronomy' is the profound truth that Newton demonstrated the movements of the planets and the stars not with a measuring device, but with the application of mathematical formulas. He demonstrated that movement and inter-reaction between objects is not something that is comprehensibile to the senses, but that there is nevertheless truth beyond the senses.
When you find yourself in an argument with someone about how nothing in the universe can be proven to be true, beath that person to death with a copy of the Principia. It's a pretty big book. It will do the job nicely.
(Yes, I know that elements of the book were later proven to be false by physicists in the 20th century, notably Einstein, but we will pick that up when we discuss the technology 'Physics')
If I may go off on a tangent for a moment (ha ha) regarding the nature of truth and mathematics, once again digging into Plato's accounts of Socrates, it is time I made mention of the Pythagorean Theorum. This is the very simple formula your grade 7 math teacher tried to beat into your head, that,
"in any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the area of the squares whose sides are the two legs (the two sides that meet at the right angle."
See? Simple.
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| Nightmare fuel. |
Nevertheless, the exactness of the formula, and the presence of perfect triangles between every particle of matter that exists, supersedes what your senses - or your measuring devices - can prove. The Pythagorean theorum IS true ... no matter what you imagine the universe to be. That is what is astounding about mathematics.
Newton was able to describe the movements of stars he could never see move, and predict the location of planets which were not previously conceived of, with pen and paper. Newton did not create 'truth' ... he uncovered it. The truth had been there all along, and if he had not done the uncovering, when the work was done by someone else, however many centuries that would have been the formulas would have been exactly the same. And that is astounding too.
It means that no matter what extraterrestrial creatures may exist in the universe, or in what number, or with what basic biological make-up, when they construct rocket engines, they use the same Newtonian principles we do. The exact same principles. Think about that.
If that doesn't give you pause, you haven't really done enough thinking.
Conceiving the principles of astronomical physics prior to those principles being observed and demonstrated to have relevance is the foundation of mathematics ... and in a way, it is the foundation of magic, also.
Let us understand - magic, should such a thing exist, is a tool that exists apart from the principles of observation and your five senses. It cannot be 'crafted' into existence; it is not an result that is achieved in the physical world. It is a conception, and by that I mean that the truth of magic is uncovered, and not created. A caster does not 'will' the cure light wounds into existence ... the caster circumscribes the laws of magic in a manner that enables the cure light wounds - which has been inherent in the wounded body since the body's injury - to overcome the apparent physical manifestation that has been observed.
I feel that isn't very clear, and it is full of conjecture on my part, since - obviously - I don't have the benefits of a Principia Supernatura ... which would be convenient, I must confess. What I'm hoping to get across is this: that although magic is not measurable, it nevertheless must function according to very specific Laws. In turn, the comprehension of these laws is not necessarily something that comes from demonstration or training.
One can imagine spellcasters sitting in a classroom teaching them the basics of magic in a very different manner than the Hogwartzian method. After all, when your math teacher tells you to conceive of two trains leaving Chicago and Pittsburgh on the same track, he or she does not ask you to take a flight to Chicago to watch the train leave. No, you are taught the fundamentals of math, so that when the day comes that you need to calculate how many porn magazines you can buy with your first paycheck at McDonalds, that math is there and ready to hand.
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| Many of the students at Hogwartz took actual classes. |
Magic ought to be seen the same way. Once you have the fundamentals of how your brain needs to be wrapped around the intrisic properties of magic, you ought to spontaneously be able to produce magic at will. Small stuff at first, since the big stuff requires a greater complexity in manipulating the quantifiers or qualifiers that make magic happen. But then it is conceivable that, upon reaching third level, you've overcome the mental block that stopped you from manipulating those quantifiers, and boom, yes, without training, you now CAN cast a second level spell. The block was never about being shown, step by step, how to cast invisibility. Casting invisibility is not making a chair. It is solving a quadratic equation that has stumped you for some time now.
If we accept that premise, than it follows that no matter what race casts magic, no matter what corporeal existence they have or what plane of existence they occupy, the magic will always be the same because the principle is inherent in the magic, and not the caster.
Not where you would expect Astronomy to go, right? Fact is, 'Astronomy' as most people understand it is an observational past-time. For Astronomers, the technology is not in the observation, but in the calculation. Thinking along those lines, 'casting' is less a physical activity than a mental one. To cast is to infuse the non-apparent reality into the apparent reality ... and thus retain the substance of a whole reality, one with elements which everyone can see, and with elements only the caster can see.
The weirdness of treants appearing out of thin air only seems impossible to the layman. To the spellcaster, those treants were there all along. The trick is to make them appear.
The idea of distilling magic into a science through the proper application of intellect is a wonderful concept to be honest. It would make sense that at some point in the history of a world, a Newton would come along and take the blinders off, so to speak, of magical understanding. Prior to the arrival of such a person, it would be easy to say that the understanding of magic was trapped in dogma or simple repetition of what others discovered in the past without fully understanding the background that went into it.
ReplyDeleteI could honestly see a sort of revolution that might come to magic in a post Newton-esque period. With the first fundamental equations and work done, intrepid scientists and researches tearing into the complete body of work that makes magic work to quantify it's mechanics. After all, you can put an arcane spell in a potion just as easy as a divine spell.
With enough time, probably outside the realm of a single campaign but easily doable in a persistent world, you might even find people willing to push the envelope and crack what makes 'divine' spells function and if it is reproducible without divine intervention.
Perhaps even the arrival of a 'unified magical theory' far down the road after enough understanding is reached, the final breakdown of the barrier between wizard and clerical based spells...
Then again, that might be the equivalent of the Physics technology.
But still, thanks for this wonderful post.
I absolutely adore this post. And agree with what Blaine above says as well.
ReplyDeleteThe way I envision such a magical theory as applied to D&D might be is quite similar to how "Myst" deals with it's magical worlds in books.
The idea being that a certain language, in the above case written in special inks on special papers, would contain the keys to reaching through the realms of probobility and "creating" the world described. The universe is infinite, therefore, somewhere, whatever described must exist.
So, in terms of the treants, the magician is merely describing to the universe a completely probable event, only improbable to those who can't speak the universe's language.
The Civ posts, incidentally, remain my absolute favorite thing to read here. It will be a shame when they've finished at last.
Spectacular.
The nearest I've seen to a principa magica would be "Real Magic" by isaac bonewitz. i'd recomend tracking down an early printing/edition of that book for a scholarly book on magic.
ReplyDeleteNewton is a hero of mine and the book fantastic but I'm the sort of nerd who laughed at math jokes and did calculus problems in my sleep during my college days.
Alexis,
ReplyDeleteFormulaic magic in D&D? Heresy. You ought to be pelted with d4s for suggesting that you could formula-ize the existing system without substantially re-writing what's presented in the PHB and DMG -- so much so that it would be unrecognizable as having been inspired by AD&D.
The D&D magic "system" (and I use quotes because it is not much of a system -- V-S-M, memorize spell, cast spell, spell gone) is the hoariest handwave of all hoary handwaves in RPGs. First, it's Magic. It doesn't make sense. It's not supposed to. It's the opposite of Science.
Consider this: an Isaac Newton of magic shows up on the scene and publishes the book you describe. How long would it be before the entire world had completely given up on engineering and math and just did everything by magic? What would prevent that level of utilization of magic?
-Carl
Heretic and proud.
ReplyDeletePutting aside that I disagree with you regarding everything you've said, except that I threw out VSM billions of years ago, I'll offer the simple answer.
Magic is more complicated than math. Not everyone can do it.
We're actually still waiting for a human that can.
This is a great post! Thanks! This makes me think of Arthur C. Clarke's Third Law: "Any sufficiently advanced technology is indistinguishable from magic." Yeah, I know--mathematics is a set of principle ontologically woven into existence and not a technology, like, say, a toaster oven. But as much as you're discussing mathemamatics as an analoque to magic in this post, you are also talking about "applied mathematics"--*cough*--I mean, "applied magic." I could be wrong, but is not engineering, computer sciences, or, any applied science that is fundamentally based on mathematic principles a better analogy to "casting" than "mathematics." Wait! I just realized I agree with you. You have the principles of mathematics (magic) and that the application of mathematics, i.e. "doing math" (casting). So there's magical theory--which is pure thought--and then "applied magical theory"--which is casting. Wow! This is a great idea! Let me compose myself before humbly tracing another thought connected to Clark's Law. *deep breath* So, I am thinking of Jack Vance's _The Dying Earth_ series, which is a strange animal becaause, for those of us who are familiar with it--it is a "science-fiction" in that it is set in the future and not in the past; and yet, the major technology of the far-flung future is not the computer, the robot, the genetic-splicer; rather, it's magic. In these stories Vance has some really interesting ideas about how the magic being practiced late in the history of the world is done by rote. The Sorcerer's organize and catalog spells; however, they don't understand the principles upon which magic is based. This sort of atavistic conception of magic is what makes the world of Jack Vance's dying earth seem so strange and decadent for me. But your reading of "magic" here totally conforms to Vance's vision; which is ironic, I think, because Vance's magic system was a major influence on Gygax and thus on D&D. Thesis: if "Clark's Law" applies to Jack Vance's magic, then it applies to D&D.
ReplyDeleteTo Carl -- I always thought the great thing about the confusing, random, and weird nature of magic in D&D was interesting because the demented and genius minds of sorcerer's understood all of its mysteries. Thus, it's only to "lay-people" that magic is confusing and strange. As far as other people being able to do it: I can't do Calculus. I'm not a deep programmer. And yet, some computer software and other technologies work for me as if by magic. So I think the analogy is nevertheless sound.
Thanks for the great post!
Writing as a graduate mechanical / nuclear engineer with more than a decade of experience ... you merely confirm my longstanding suspicion that liberal arts provide sufficient foundation to understand the "hard" sciences, given interest.
ReplyDeleteCurse my wasted years of manipulating the same equations to different purposes.