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In the most fantasy settings there is a binary structure of the ways to achieve some practical goal, namely "magical" and/or "technological" one.

For example we have a goal to remove a mountain top, so there are ways:

  • To pronounce arcane words and divert the energy from ethereal dimension into the caster's realm to blast the mountain top (magic);
  • To pray to some deity and plead them to remove mountain top (magic);
  • To use earth-moving machines to dig down mountain top (technology);

I see other option in probability manipulation / boosting, like person is wandering around the mountain doing nothing, thinking nothing but mountain top collapses itself (probability almost zero, but not exactly zero), like in White-Luck Warrior (Bakker) or Niven's Ringworld.

What kind of other worldbuilding's paradigms can be used in lieu of "magic" and "technology"?

--- EDIT ----------

I checked Meta and there's a huge corpus about "opinion-based questions" and understood that I need to setup some restriction to the question and also some "objective function" to evaluate the "best" question. For the question posed by me seems all the answers eligible for acceptance.

So let me give some definitions:

Definition 1: "Technology" is a means to transform subject's intention to achieve external goal through, at first, creation of internal model (symbol, blueprint), then, after it by the use of an external tool.

Graph format: Volition -> Symbol (Model) -> Tool -> Profit.

Examples: Prehistoric man kills prey with its own hands; the hobbit tries to spy at Sauron through the palantir; an alien race grows genetical modified trees to use them as starships; a politician uses propaganda to mobilize population to raze the mountain-top.

Definition 2: "Magic" is a means to transform subject's intention to achieve external goal through creation and manipulation of internal model (symbol, blueprint), without the use of an external tool.

Graph format: Volition -> Symbol (Model) -> Profit.

Examples: A necromancer raises an army of dead through concentration and will power; Magneto bends electro-magnetic fields and pull an asteroid to the Earth; Gandalf breaks Saruman's staff from the distance.

Restrictions to the answers:

  • The subject should be sentient and must have an intention;
  • External result is obligatory.

"Objective function" to judge the best answer:

  • Present definitions of the alternatives to "magic-technology"duality;
  • Present examples, which illustrate the definitions;
  • Optional. Reference to some fantasy / sci-fi / philosophy treatise.
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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – L.Dutch
    Jul 16 at 2:41
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    $\begingroup$ There's nothing else besides natural (technology) and supernatural (magic). $\endgroup$
    – RonJohn
    Jul 16 at 2:57
  • $\begingroup$ ...or to put @RonJohn 's comment in your newest terms: Definition 1 covers the case where you do use external tools. Definition 2 covers the case where you do not use them. It's kinda binary: do or do not, there is no middle ground. $\endgroup$
    – A C
    Jul 16 at 4:24
  • $\begingroup$ ...unless you've got some kind of energy field which is created by all living things, and is simultaneously around them and inside them. I guess a force such as that might blur the line between using an external tool and not using one... $\endgroup$
    – A C
    Jul 16 at 4:37
  • $\begingroup$ @AC What about "try"? :) $\endgroup$
    – Barmar
    Jul 16 at 13:53

32 Answers 32

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This started as a comment on Ash's answer, which challenges the statement that "divine power" is just magic by another name. I'm expanding it here to try and achieve these aims:

  • To use OP's "graph" structure to classify and propose new options that may answer the question.
  • To provide examples from literature or folklore to back these up. (There is currently a request for "canonical" answers. I don't know what "canonical" ought to mean in the context of this StackExchange site, but I suppose "how other authors have done it" counts.)

Please feel free to suggest additional examples in the comments!

Definitions

Here is how I understand the terms in OP's graphs.

  • "Volition": There is a thinking entity who desires the completion of the task.
  • "Model": A concept or plan for how to go about the task.
  • "Tool": The use of matter to effect a change through physical processes.
  • "Profit": The accomplishment of the task.

And I add one more:

  • "Request": An appeal to another thinking entity to complete the task.

Technology

Volition → Model → Tool → Profit

Examples:

  • Reality and hard science fiction. Levelling the mountaintop by bulldozer, dynamite, laser cannon, or just moving a single pebble at a time by hand.
  • Sympathetic magic. Many "real-world" examples; thaumaturgy in Butcher's Dresden Files; sympathy in Rothfuss' Kingkiller Chronicle; arguably Wilde's The Picture of Dorian Gray.
  • Probably other magic systems with a quasi-scientific explanation.

Magic

Volition → Model → Profit

The distinction is the lack of a physical means for the process to happen. As we know from Clarke's third law, it's difficult to draw a line between technology and magic... so I'm not even going to try. I'll just say that "magic" is when there is no explicable process by which your intention (Model) is made reality (Profit). You conceptualise what you want done, perhaps formalised in "casting a spell", and it just... happens.

Examples: Difficult to identify, because so many works try and explain their magic.

  • "The Will and the Word" in Eddings' Belgariad and Malloreon series is the clearest example I can think of: picture what you want done, speak a word (any word), and if your will is strong enough, it happens.
  • I think anything that talks about a generic "magic power", without trying to define it as some sort of energy, can come under this. The "One Power" in Jordan's Wheel of Time series; the "Weave" in Forgotten Realms.
  • By my definition of Tool, whether a magical implement like a palantír counts as Magic or Technology depends on whether there is any explicable process underlying it. We frequently don't have enough information to decide either way. I'd lean towards palantíri being Magic.

Intervention

Volition → Request → Profit

Any request (or command, prayer, labour contract...) to another thinking entity fits in this graph. Thus, this encompasses both Divine Intervention and Political Power. The other entity must have some means of accomplishing the task, of course, also selected from this list.

Examples:

  • Prayer in religion and mythology.
  • Certain interpretations of divine magic in Dungeons & Dragons. For most purposes, this is treated the same as arcane magic: cast spell, achieve result. However, there is an implication that the "spell" does not compel the result, but is a request for a divine power to intervene—a request that may be refused or reinterpreted.
  • Since I already mentioned Eddings, his Styric magic (Elenium and Tamuli series) counts. It looks like Magic, until at least one protagonist realises he doesn't have to use the formal, prescribed spells... he can just politely ask. He's chided for bad form, but it works.

Deific Power

Volition → Profit

A "deity" in this sense is a thinking entity who shapes reality by simply wanting something to change. They need no Model, no plan or conception of how to go about effecting their desire. Their will is reality.

Examples:

  • Some, but by no means all, concepts of "gods".
  • Perhaps Orcs/Orks in Warhammer (Fantasy and 40K). Notably, they may add a Tool to the graph, but it doesn't seem to actually do anything.
  • Perhaps Le Guin's The Lathe of Heaven.

Luck

∅ → Profit

Without the thinking entity even willing it—or willing it, but not desiring it, in some vaguely Zen sense—circumstances conspire to bring about the result that suits the entity.

Examples:

  • Mat in Jordan's Wheel of Time.
  • Felix Felicis in Rowling's Harry Potter.
  • Cthulhu waiting for the stars to be right.
  • Maybe Rincewind in Pratchett's Discworld, though the unasked-for attention of the Lady (the luck goddess) complicates this.
  • Maybe some examples in Butcher's Dresden Files, though again unsought divine intervention is a factor.

Other combinations

Volition → Tool → Profit: You bang away at it without any clear idea of how or why it works. Computer programmers fit here more than they'd like to admit.

Volition → Model → Request → Profit: Equivalent to Intervention, except we're including the fact of the original entity making the plans. Slave labour and "throw minions at them by the thousands" tactics go here, unless you consider the slaves/minions to just be a Tool.

Model → Tool → Profit: You don't want it to happen, but must comply with someone else's Request. Drop the Tool if you accomplish it by Magic.

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It's worth remembering Arthur C. Clarke's old quip:

Any sufficiently advanced technology is indistinguishable from magic

And by corollary, any sufficiently understood magic is indistinguishable from technology. In the end what we always have is the control and manipulation of some form of energy (through some series of transformations) to produce a desired result.

  • Do we control fire to produce gas expansion that pushes a piston which turns a gear which rotates a tire?
  • Do we focus and pattern light using mirrors and prisms to send it down cables to diodes that convert it to electricity that moves a speaker that we hear as sound?
  • Do we gather some ethereal magical energy so we can structure it with runes and incantations and convert it some desired effect?
  • Do we use our minds to communicate with and command living things (animals, insects, birds, fish, people...), channeling the power inherent in life to do our bidding?
  • Do we discipline our bodies, minds, and souls as a religious offering, so that some god will use its power to grant miracles on our behalf?

In every case, we are developing a control system that will guide and convert raw power into applied force. There is no dichotomy between magic and technology; the Palantír of "The Lord of the Rings" might just as well be an iPhone; they'd both seem like magic to the hobbits.

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    – L.Dutch
    Jul 16 at 13:50
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Biology

In order to achieve a practical goal, biological mechanisms could be used. On the lowest level, this would be just existing and moving around, not very exciting. On a slightly higher level, that would be some self-improvement (e.g. working out to build stronger muscles) and using other creatures (e.g. horses). This is slightly better, but it is not very impressive (probably because it has already been done since the dawn of the civilization). Sadly, with known currently disposable means, there is not much room for significantly more impressive "biological manipulations".

However, in the speculative fiction worldbuilding, currently available/known biology can be only a subset biological things to play with.

So one can introduce additional creatures, with impressive abilities, or some symbiotic organisms with a performance unlike anything currently known on Earth, which could effectively give something like superpowers. Also, keep in mind that, when able to grow, life often grows exponentially, which could potentially result in an immense power from a relatively humble-looking starting point (e.g. a wielder of biological powers spreads something to grow many order of magnitudes larger than themself). Large usable structures, such as buildings and ships may also be simply "grown" in a similar manner. Maybe even something advanced like spaceships, resulting in 8472-esque organic-looking bioships.

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    $\begingroup$ This is for sure a third way. 1: blast with magic 2: remove with tech 3: army of people with shovels and baskets start digging. $\endgroup$
    – Willk
    Jul 13 at 17:06
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    $\begingroup$ @Willk Shovels and baskets are also technology. To really do it the biological way, you should use your bare hands, or an army of trained moles. $\endgroup$ Jul 14 at 6:36
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    $\begingroup$ @user3153372 - its about time that army of trained moles earned their keep. It took forever to train them! $\endgroup$
    – Willk
    Jul 14 at 14:33
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    $\begingroup$ On one hand I like this, because it is definitely gives a very different flavor to a story than either robots or runes. On the other hand, animal husbandry/training and genetic engineering are very much technologies, and the presence or absence of pre-existing biology that does what you need it to do is basically magic. So it strikes me as just a particular point on the continuum that OP describes, rather than outside of it $\endgroup$
    – BThompson
    Jul 14 at 20:13
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    $\begingroup$ Biology + Time *(mutation / natural selection) = Evolution. $\endgroup$ Jul 15 at 1:23
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The Divine

  • I can make a bow & arrow to attack at range. That's tech. Turning knowledge and resources into an action.
  • I can cast a magic missile. That's magic. I gather mana and use it and knowledge to turn that into an action.
  • I can ask God (or a god) to smite you. That's divine intervention. I gather favour with the gods through devotion, faith, and or sacrifice, and God performs the action for me.
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    $\begingroup$ The OP seems to have covered this idea with "pray to some deity to remove the mountaintop". He classified this as magical. $\endgroup$
    – Demigan
    Jul 13 at 16:32
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    $\begingroup$ This is a good answer, and would be better if you explicitly noted that you are challenging the OP's assertion that divine intervention = magic. Given OP's graphs of Tech = Volition → Model → Tool → Profit, versus Magic = Volition → Model → Profit, you might say divine intervention lacks a model: Volition → Request → Profit. Of course then there's the question of whether the deity's exercise of power fits under magic. I'd say god-like power implies a fourth graph: Volition → Profit. $\endgroup$ Jul 15 at 6:40
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    $\begingroup$ @Hobbamok indeed, I once read a trilogy in which the gods secretly were just amazingly powerful magicians, having honed their abilities to the point of becoming immortal $\endgroup$ Jul 15 at 13:06
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    $\begingroup$ @Artem I think the main difference between "magic" and "divine" in my mind is the added dimension of the god's personality and the relationship between them and the caster (assuming the god is a person). If you bang atoms together in the same way, you'll always get the same result. But asking a person for something can take many different forms: "I'll have a BLT, hold the mayo, please," vs. "Can you please help me with me homework?" vs. "Look, I'm sorry about last time! Give me another chance!" vs. "...Will you marry me?" ...and their responses may or may not be predictable. $\endgroup$
    – Qami
    Jul 15 at 18:00
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    $\begingroup$ @Artem: Dark Souls isn’t alone in treating mages and clerics as doing the same thing (magic) with a different power source. Dungeons & Dragons is another example (and one that's influenced many others to do the same). I happen to dislike the idea that divine magic is exactly the same as arcane, with rote prayers compelling a result. Gods as vending machines: "say prayer, receive smiting". And while my (dis)likes aren't material here, I do think drawing a distinction can give you the third option you asked for. $\endgroup$ Jul 15 at 18:37
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The most common of all Natural

A large meteor slams into the mountain top? Natural.

Avalanches/water erosion over time? Natural.

Destabilization of the mountaintop leads to collapse?

Mining operation causes issues?

Natural is common.

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Fate

The mountaintop will be removed. It's going to happen--circumstances both mundane and extraordinary have just seemed to line up to pave the way, and any effort to prevent it is either stymied by other unexpected circumstances, or turns out to have been a necessary part of the process for it to happen.

Is it technology? Maybe some parts of it involve technology, but you're starting to suspect that it would happen anyway if those parts weren't available.

Is it magic? It feels like it, but there have been no observable violations in the laws of physics. If a god is making this happen, he's keeping his hand well-hidden.

Is it probability manipulation? This is perhaps the most likely suspect. But if so, again, who's doing the manipulating? There's no apparent reason why this should happen, no cause we can trace it back to. Unless!...no, it's too far-fetched...but yeah, perhaps I'm in a story, and the author needed this to happen as part of a grand plan? That would explain it.

The catch is, of course, that fate works the other way around from your technology and your magic. You don't use fate, it uses you. (Regardless of whether or not you find yourself in Soviet Russia)

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In the end it is all a system you try to use in the story.

Digging that mountaintop down is the use of physics in ways we understand. We might not know the internal workings of an excavator, but we know how an excavator more or less works.

Magic is simply the addition of a new set of physics, often only partially understood. It allows the story to do fantastical things, but still understandable things within the rules established in the story.

Not all magic is classified as magic though. Hyperspace, warp travel, slipspace, traveling through what is essentially the dimension of hell or other forms of FTL are all magical, but displayed as technological. Other things are more obviously magical, but don't have to be classified as such. The Force for example. So it comes down to how ridgid you want your classification to be: is anything with extra physics magic, or can it be subdivided in more categories? Examples:

  • magic
  • religion&faith
  • innate abilities and gifts (say the Basilisks stare, werewolf healing, the X-men abilities or the ability for Dragons to fly despite a small wingspan and low flapping frequency)
  • technomagic
  • steampunk (a form of technomagic)
  • telepathy&telekinesis (often lumped together)

You can probably think of some yourself.

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    $\begingroup$ It is customary to wait 24 hours before accepting an answer. That gives people all over the world a chance to try to answer your question. Accepting early discourages players from answering it, and they might have a better answer than this! $\endgroup$
    – Demigan
    Jul 13 at 14:11
  • $\begingroup$ Thanks, Demigan, I unaccepted the answer, will follow your advice. $\endgroup$
    – Artem
    Jul 13 at 18:25
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Non doing.

https://alongthetao.wordpress.com/2012/11/12/37th-verse-do-nothing-leave-nothing-undone/

The Tao does nothing, but leaves nothing undone.

If powerful men could center themselves in it

the whole world would be transformed by itself, in its natural rhythms.

Wu wei - "non doing" is less "doing" centered and goal oriented. Perhaps more holistic, to borrow a later word?

https://www.theschooloflife.com/thebookoflife/wu-wei-doing-nothing/

Wu wei is closely connected to the Daoist reverence for the natural world, for it means striving to make our behaviour as spontaneous and inevitable as certain natural processes, and to ensure that we are swimming with rather than against currents. We are to be like the bamboo that bends in the wind or the plant that adjusts itself to the shape of a tree. Wu wei involves letting go of ideals that we may otherwise try to force too violently onto things; it invites us instead to respond to the true demands of situations, which tend only to be noticed when we put our own ego-driven plans aside. What can follow is a loss of self-consciousness, a new unity between the self and its environment, which releases an energy that is normally held back by an overly aggressive, willful style of thinking.

The student of the Tao would not pray to a deity, or use magic incantations, or muster an army of diggers. Perhaps the student would strive to understand (or understand without striving) the top of the mountain, and what is underneath. Or if not understand, perceive and appreciate. The student would see how the mountain as it exists can be harmoniously incorporated into the plan. Which might no longer be a plan.

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    $\begingroup$ Actually, good point, seems that "magic-technology" dichotomy is a part of Western worldview. Seems worth to dig deeper into other cultures perspectives. $\endgroup$
    – Artem
    Jul 13 at 21:09
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Political Power / Charisma / Psionics

I know this probably is far afield of what you had in mind, but it strongly bears mentioning, especially in fantasy settings. If you're a Pharoah or another type of ruler, you need neither technology nor magic if you have enough strong bodies who are either willing or forced to do the hard manual labor.

This can be accomplished directly by Political Power, or directly/indirectly by Charisma or Psionics.

Let's take Psionics first. Some might argue this is "magic" but if the author postulates that it is, in fact, a biological or physical trait, then it's a question of which way the reader chooses to perceive it. Psionics might be used directly: "Hey, wouldn't it be a good idea for you and all your buddies to go dig out and level that mountain?" But you'd have to do this to a LOT of people.

Psionics could also be used to achieve Political Power, which might be more convoluted, but is probably more efficient in the longer term. You can imagine how someone could [mis]use such a capability to become politically powerful.

Next, consider Charisma. The strongly charismatic character can often convince others that actions they'd normally never consider are, in fact, a good idea. This works almost the same way as Psionics except that it isn't metaphysical, and the recipient is at least a partially-willing participant.

Thus the same arguments hold for Charisma: our (Machiavellian) character is probably better off using it to achieve political power first. Otherwise you have to talk to and convince a LOT of people.

Which brings us back to Political Power.

  • If you are a dictator, you can simply order your subordinates to plan and execute the removal of the mountain by whatever means necessary. You need not even concern yourself with how they'll accomplish it, though their solution (in a primitive setting) likely involves conscription or outright slavery.
  • If you are a person of lesser power within the organization of a dictator or monarch, you need to earn brownie points with your allies -- and collect dirt on your enemies -- so that both groups cooperate with you when you propose your plan to the leader. If you're a GREAT manipulator, you maneuver others into deciding to do your idea(s) for you. This is even more effective, because if anything goes wrong with the plan, you were the person saying it was a bad idea all along, and others end up taking the blame.
  • If you are a duly elected official, you will still use such sneaky and underhanded --- sorry, I mean cleverly bipartisan --- means to build your power base and accomplish the goal of flattening the mountain. This might be a lot more difficult than the other two possibilities because you also must find the funding to pay the workers who will be hired to do the physical labor!

Use of Political Power can become very ugly, very quickly. But it can get things done that were otherwise not possible.

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Frame Challenge: the definitions provided may overly restrict the desired answer. Please allow me to propose some changes

Definition 1: "Technology" is a means to transform subject's intention to achieve external goal through, at first, creation of internal model (symbol, blueprint), then, after it by the use of an external tool.

I propose that the tool is not required.

Graph format: Volition -> Symbol (Model) -> Tool -> Profit.

Examples: A hostage negotiator uses his training to talk down a bank robbery; a banker uses best-practices to close a deal; a politician uses propaganda to mobilize population to raze the mountain-top.

Likewise, I propose that "technology" may use either internal or external models to accomplish the task.

Definition 2: "Magic" is a means to transform subject's intention to achieve external goal through creation and manipulation of internal model (symbol, blueprint), without the use of an external tool.

Graph format: Volition -> Symbol (Model) -> Profit.

I propose dropping this definition entirely, in favor of the following:

Graph format: Volition (...) -> Symbol (...) -> Profit (...)

The Familiarity Axis (Profit)

What we're trying to achieve (profit) can be mundane, or pretty weird. Because our profit target can be vague, getting profit that we are happy with at the end of the day depends on how weird is being shot for. Here are some bands along this axis:

  • The familiar are things like saddling my horse, or tightening a sail. I don't have to understand how they work (symbol/understanding), and I don't have to be the one to do them (volition/agency). Familiar profit goals are easy to assess, and the profit will be what you asked for (most of the time)

  • The unfamiliar are things like a skunk being able to emit an overpowering stench, or an eel being able to shock you, or ink from a squid, or poison from a viper. I can still work with the unfamiliar to achieve an outcome - I can harness squid ink; or viper venom; I can put skunks on my trail to deter hounds; I can use hound's incredible sense of smell to find lost people. However, the unfamiliar may not always, even when used properly, get me my profit.

  • The alien things are inexplicable. Like life at the bottom of the deepest ocean trench; or the processes beneath the earth. Again, understanding of alien things is not required to profit : I need not understand Raleigh scattering and microstructures to use opals; or mine diamonds to be used for their characteristics; I can use smallpox blankets to attack my enemies without understanding anything of germs; and I can use the golden extract of a certain kind of bread mold to help heal infections. However, the alien are least likely to get me to my profit. In fact, my familiarity with alien things is so dim that someone might trade my smallpox blankets for clean blankets, or my clean blankets for plague ones, entirely without me being able to tell the difference.

Graph: Volition (...) -> Symbol (...) -> Profit (familiar/unfamiliar/alien)

The Understanding Axis (Symbol)

How much do I understand (have the symbols or mental models) the actions I am taking to get the profit? Here are some ideas:

  • At the level of technology, I have accurately-enough defined every variable; resolved every important paradox; and simplified the core relationships into something anyone can use at their writing table. I can make designs and evaluate them against theoretical minimums and maximums.

Technology can be unfamiliar - I can use some kind of stimulant to get an eel to shock, but I am much more likely to use my better understanding to switch to a familiar alternative like blasting lightning out of a generator.

  • Understanding can be less precise as Art. Some concepts are defined, but whether the things that have definitions are the simplest expressions is still undetermined. There are paradoxes that we have not identified the language to express and overcome, and these paradoxes keep us from precision modeling. Instead, we use expensive trial-and-error to "walk our fire" to profit, usually over many unprofitable iterations.

  • And at it's least precise, understanding is Magic. It might be possible to stand on a certain field during a storm and call lightning from the sky. A technologist would know the field your standing on has natural conductive and insulating layers turning the area into a natural battery, that is getting charged by the storm overhead. But a magician just can imitate the things he or she saw that caused the effect last time.

Graph: Volition (...) -> Symbol (technology/art/magic) -> Profit (familiar/unfamiliar/alien)

The Agency Axis (Volition)

Who is doing this, anyway?

This is a very important distinction. You might ask - “why?”. Using other agents gives you access, potentially, to broader perspectives or better information. You may not get the profit you had in mind when you engaged these others; you may get something BETTER . Something beyond your imagination. You may:

  • Appeal to your self. Obviously, you are the one seeking the profit. And limited by your understanding and the familiarity of what your intended outcome is.

  • But you may appeal to a group. A group may just be you and the monster under the bed working together; but you are at a minimum an essential co-partner in the action. Maybe the nukes just can't be launched with a single key. A group might be semi-divine such as spirits of your ancestors, or outright divine like elementals, nature spirits, or deities. The others in the group have the option to decline your request. You are sharing agency, and may be able to get by on only a little help.

  • Finally, you may appeal to someone else. You have given up agency; your volition is not driving the profit. You might make a request, but the someone else might have taken action regardless. Someone else might modify the plan slightly to include you, or may say "no". Someone else may even choose to work against your profit.

Graph: Volition (I/us/you) -> Symbol (technology/art/magic) -> Profit (familiar/unfamiliar/alien)

Some Final Graphs, and Examples

Graph: Volition(you) -> Symbol(magic) -> Profit(alien) : prayer for a miracle from a deity. The seas part; you walk on water; the aliens blast a mountain with their ray guns

Graph: Volition(you) -> Symbol(magic) -> Profit(unfamiliar) : taking a sick child to healing springs; or a medicine man; or a unicorn; a fairy, or a questing beast

Graph: Volition(you) -> Symbol(magic) -> Profit(familiar) : leaving an enemy out in the desert for the beasts and the sun to get him or her.

Graph: Volition(you) -> Symbol(art) -> Profit(alien) : a prayer uttered over a sketchy rope bridge made of rotting jungle wood and improvised vines

Graph: Volition(you) -> Symbol(art) -> Profit(unfamiliar) : a gambler playing the odds at a table; a military strategist estimating losses in an upcoming engagement; an adventurer stepping into the unknown with only the god(s) and their wits at their side

Graph: Volition(you) -> Symbol(art) -> Profit(familiar) : complaining to the local magistrate of problems in your town; politics within your peer group (maybe something dazzling like anti-matter physicists)

Graph: Volition(you) -> Symbol(technology) -> Profit(alien) : sending money or a note of approval to a crowd-sourced volunteer effort to cure hunger; or poverty; or a group tagging great white sharks on the other side of the world.

Graph: Volition(you) -> Symbol(technology) -> Profit(unfamiliar) : sending a note of encouragement to a group that is attempting to drill wells; or set up cell towers in the remote rural parts of this world.

Graph: Volition(you) -> Symbol(technology) -> Profit(familiar) : donating to your local second-hand-goods store or food bank, with an intended profit of getting those goods offered for resale.

Graph: Volition(us) -> Symbol(magic) -> Profit(alien) : allowing yourself to be possessed by a spirit, deity, or strange brain symbiotic so that you can obtain power to avenge the destruction of your homeland; you supposedly retain the power to throw off the possession, so your willing on-going participation is required.

...

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  • $\begingroup$ Wow. This bears re-reading multiple times, because it offers a highly rational and detailed FRAMEWORK for thinking about the background of the original poster's question. I'm printing and keeping this. $\endgroup$
    – Forbin
    Sep 16 at 19:38
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I think the magic vs technology breakdown is a bit problematic, because the lines between technology, nature, magic and divine or supernatural entities can be quite blurry, and magic in itself can have varying definitions.

I would rather break it down into natural and supernatural (which probably roughly corresponds to what you call technology and magic).

By definition, this is all that can exist. Either something is within nature or it is not. Either it is natural or it is supernatural. Well, it could be both, but there can't exist anything besides those 2 things, since the one by definition includes everything the other doesn't.

Natural

Anything that fits squarely into the laws of nature.

This includes:

  • Pretty much anything any natural beings are capable of doing or creating. This includes a billion ants getting together and digging through a mountain top as well as a human building a machine to do so.
  • Any natural effects (storms, earthquakes, magnetism, etc.).
  • Any force or effect by a natural being that only interacts with the natural world. I can use my hand to lift something up. That only interacts with the natural world. This is specifically intended to clarify magic-like forces (e.g. manipulating, observing or creating objects in the natural world purely through our minds). Those would also classify under this category if you were to include them fully within the natural world and give them a natural explanation (as opposed to having them be partially or fully supernatural). This is probably what something like the X-Men (and many modern superhero stories) is going for, where powers are explained as being purely related to physical mutations.

Supernatural

Anything that can manipulate the observable universe, but exists fully or partially outside the observable universe. Things that would violate the physical laws of the nature (not the laws as we know them, but as they exist).

This might include:

  • The natural drawing from the supernatural: those in the natural world drawing on or possessing forces outside the physical world (i.e. certain interpretations of magic).

  • Independent supernatural forces: Gods or similar beings. Ghosts may be included here, or they may be considered natural (depending on interpretation).

  • Manipulating the natural world indirectly: Those in the natural world manipulating the fabric of reality directly (i.e. getting into and changing "the code" of the universe, by e.g. causing a paradox or otherwise "breaking" the universe through natural / technological means). If humans naturally possess this ability, a good argument can be made that this is part of the natural world, they are drawing on the supernatural or they themselves are supernatural (think Neo in The Matrix, who can do "supernatural" things within The Matrix, but arguably only because he had an existence outside of it).

I don't believe there is any supernatural force that would fall outside of all 3 categories mentioned above, as they are very broad and based on the different ways any 2 things A and B can interact with one another (those things being natural and supernatural in this case): A affects B, B affects A or A affects itself. But I might be wrong.

This definition of supernatural might arguably also be problematic, since something's existence and ability to affect the observable universe might necessitate it's inclusion in the laws of the nature, and something doesn't need to be directly observable to be a fundamental part of the laws of nature, but I think it does a good enough job to demonstrate something distinct from what we typically consider to be "natural".

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    $\begingroup$ This. Unless OP is talking about some specific fantasy setting, "magic" is a catch-all term that is applied to everything that is not grounded in science. By the law of the excluded middle, there is no other category. Deities acting with divine power is just one flavor of magic; telepathy and other supernatural mental powers are just another flavor. It is only within specific fantasy settings that the category "magic" is redefined (arbitrarily) to exclude specific sub-categories of the supernatural. $\endgroup$
    – Tom
    Jul 15 at 23:44
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You defined the Technology as a chain of Volition -> Symbol -> Tool -> Profit, basically meaning that to achieve a goal one has to know how to do it, and need some external tools. This is a very broad definition which includes all actions which require some kind of external support. Alternatively Magic was given as Volition -> Symbol -> Profit which omits the tool to achieve the goal. The final modification can only be to remove the Symbol, that is allow the subject to achieve his goals by the act of desiring it only.

Force of will

Graph format: Volition -> Profit

Definition 1: "Force of will" is a mean to transform subject's intention to achieve external goal through the mere act of intending a thing to happen. Under this paradigm "I desire it" implies "It happens". This can be either unconditional or has some additional requirements not connected with a Volition itself. In this paradigm one do not prepare beforehand to achieve specified intention but may instead gather authority to make this goal happen just because one so desires. (the graph may be alternatively given as Preparation -> Volition -> Profit)

Examples: In the Book of Genesis we read God said, “Let there be light,” and there was light. The was no model or knowledge of any kind involved, the mere volition of the character was enough to make things happen. Jacek Dukaj in the book Other Songs presents the alternative universe governed by the laws of Aristotle's physics. Things are made of Matter and Form, beings (mainly characters) with strong form, powerful and noble minds, influence not only the form of others, but also the matter around them by the act of their presence only. Trees grow when the great gardener walks by, they burst into flames when the powerful warlord is near and weaker characters are easily bend to the form of the stronger. Characters influence the world and can achieve their goals without any direct actions or preparations aimed at the specific task.

Comment: The magical example of Gandalf may also qualify into this paradigm. Gandalf did not explicitly cast a spell on the Saruman's staff, his mere authority was enough to make the staff break.

Above scheme is the most basic paradigm satisfying both restrictions - there is a sentient subject with an intention and there is a result. Theoretically one could extend the chain by adding new elements, but if Symbol represents conscious internal requirements and the Tool represents external requirements, then any new elements will fall into these two categories.

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There are a ton of good answers here, but I'd like to point out one more:

Political

Politics is a huge force in pretty much anything happening. Sure it could be classified as technological, but it's really too different from what most people think of as technology for that to stick.

For good or worse, politics is likely to affect any major decisions made in any technological and/or magical world.

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  • $\begingroup$ The power of persuasion and the art of compelling people to do things could be just psychological, not necessarily political. Nevertheless, I'm happy to see persuasion as being suggested as distinct from technology and magic. $\endgroup$
    – Wyck
    Jul 16 at 15:50
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(this is actually rather a comment, but the text would not fit)

Technology and magic are on the same axis

Opening: "we have a goal to remove a mountain top (..) What kind of other worldbuilding's paradigms can be used in lieu of "magic" and "technology"?"

This is difficult, because of your mountain top example. I cannot think of any other way to remove a mountain top, except through technology or by ways of magic. I think magic always serves the role of technology supplement. The two are not actually different. Either method could remove that mountain top.. and there is actually nothing "in between". Where technology stops, the magic starts. Technology and magic are like the plus side and the minus side on an axis, rather than two isolated points, allowing to find a third point somewhere. Imho, most answers here tend to put light on other axes rather than provide for alternative approaches for mountain top removal.

EDIT 15-JUL

Opening: "present a logically consistent framework which allows to generate new paradigms besides "magic-technology" dichotomy."

I now understand other goals could be considered as well, as long as it fits in the scheme. Thanks ! Action is to be initiated by a human will (Volition), there is an awareness phase (Symbol) and the goal itself should be reached (Profit).

Examples not needing technology or magic

  • Volition (child) -> Symbol (good timing, be nice) -> sex -> Profit

Suppose we'd like to travel to the moon.

  • Volition (go to moon) -> Symbol (dream image) -> jump high -> Profit

For removing a mountain top, a scheme could be applicable, without magic or technology. Just postulate a hypothetical "time gate" phenomenon.. no human made tool, prehistoric humans can use it..

  • Volition (top gone) -> Symbol (find time gate) -> go through time gate -> Profit.

One example that comes to mind is a person suffering from psychosis, setting out to heal and work again. For some people, this could involve taking medication (applying technology) others will pray (apply magic). Apart from these options along the T-M axis, these patients reach their goal through

  • Volition (feel coherent) -> Symbol (accept dependency) -> seek help -> Profit.

The axes that play a role here have to do with individuality and also with economics, that is the availability of experts who can help.

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Craftsmenship

Which in your typography, would be something like

Volition -> Tool -> Profit

So I appricate you've sort've defined this as technology (Prehistoric man kills prey with its own hands) but I think you should reconsider.

While this is arguably technology that the society has just internalised sufficently to 'stop thinking about it', I feel that distinction is very worthing highlighting. This is how people have done things for most of human history, the basket weaver and the potter aren't making any precise measurements as they work, they've simply done this their entire lives, they don't need to draw a diagram, they have just the muscle memory and process down to an artform. None of that is what I'd call 'technology'

You might think the applications of craftsmenship are relatively small, that it could never get you to the moon but that's just due to what we have traditionally considered craftsmenship. Imagine an airplane factory, run in a traditional fordist model each worker is given an assigned task (layering carbon fibre sheets, casting engine blocksk, sanding and polishing wings), at first the managers and R&D staff are constantly looking to refine the process as much as they can, eventually though the process is so refined that no further research leads to any profit gains.

The shareholders fire all the managers and R&D staff to cut costs, the workers keep coming in and doing their little part of the process. Eventually their children come and join them as appretences. After a few generations nobody in the factory understands how a plane works. They don't care, they don't need too. Each worker is a lifelong disciple of their given task, it is second nature to them, and the planes coming off the production line are finer than they have ever been.

They are like the medieval brewer, who knows beer doesn't give you dysentry, but hasn't the slightest bit of an 'internal model' - and would look at you funny if you suggest otherwise.

Automation

Technology/Magic/Craftsmenship/Other -> Tool -> Tool -> Tool.... -> Profit

Again I suppose you could call this just technology in another guise, but I think there is a remarkable psychological difference between the astronaut who physically controls the machines around him to keep himself comfortable and one that whoose wants are known by the ships AI even before he realises he has them, and tended to appropriately.

Outsourcing

Just hire somebody to do it. Or in your typography

Violition -> Exchange -> Profit

Perhaps not something you can base an entire world around, or is it? It's perfectly possible outsourcing could mature to the point the privellaged class of commercialites might entirely forget who they're outsourcing too, how thoose people do what they do. They simply look at their catalouge, see everything availible, buy what they want, and which it pop out of another dimension. Like amazon, but it's really taken over the world.

They get the capital to do this from investments they got through investments they got through investments... ad infinitum, not a single person on the whole planet actuallyunderstands the technology or magic they are outsourcing this too, only that dollars get you places baby!

Trial and Error

Volition -> Many Tools -> Profit

I'm reaching now, aren't I?

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    $\begingroup$ The idea of craftsmanship (Tool without blueprint or preconception) is quite interesting. It is like illiterate idiot savant, never been outside his village, singlehandedly takes U2 plane afloat and lands sucessfully in Soviet Union without any preconception of the aircraft control and navigation. $\endgroup$
    – Artem
    Jul 15 at 19:09
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    $\begingroup$ I was going to suggest "money". So I'm happy to see outsourcing in your answer. $\endgroup$
    – Wyck
    Jul 16 at 15:47
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Scale

Instead of using earth-moving machines, you enlist millions of people with hammers in a massive public-works project to remove the mountaintop.

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Well probably the dualism is due to the fact that every other "force" can be reduced to one or the other.

Let's consider some abstract basic definitions:

Technology is the way to do something using forces that can be modeled scientifically.

Magic is the way to do something using forces that cannot be modeled scientifically.

Note that ancient people used technology even if they didn't know the underlying scientific model, i.e. fire. Even if they considered it magic.

So this is the main difference between tech/magic and this holds true regardless of the "universe" you are in. There have been a lots of "worlds" built by many authors, with magic described in a wildly different ways. But at the end, if the "magic" forces used are amenable of a scientific explanation in-universe, then it's not really magic, but poorly-understood technology.

If, however, the in-universe forces that are channeled as magic cannot ever be explained by science, then that's true magic.

Not that "explained" by science doesn't mean that you can't devise ways to study and classify them in a systematic ways. I mean, they are true magic if there is no "ontological" way to build a physical theory (with however complicated math) that explains how magic works and allows to predict its effect.

The source of the forces/power is irrelevant: divine, "classic" magic a la Gandalf/Potter, Mental/Psionic, Mystic. If you can't build a physical model it's magic, otherwise it's disguised tech as fire was for the ancient people on Earth.

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I can imagine a universe where its an inherent part of the structure that reality responds to sentient life - without being alive in a sense we know it, it responds.

That need not be magic, though it may seem so to an outsider or ignorant person. To those accustomed to it, it would be an everyday thing, to quickly set reality with a thought, when leaving for the office, so that something has a greater chance of working as desired.

I wouldn't classify that as magic (its just how the universe works, and is mundane not arcane, there's papers studying how that universe's quantum fields or equivalent are responsive), nor technology (it doesn't need devices to achieve), nor divine (no deities)....

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Magic, technology and what else?

Magic vs tech is a western fantasy dilemma, I've met other paradigma elsewhere. Most of them introduce a third factor in the process of deeds. Volition > Symbol > Interaction > Result

EMPATHY

The world is a living being, you can debate with it to have the mountain flat out.

WILLPOWER

Reality reply to consciences, and morph accordingly. As people doesn't care that stormy mountain anymore, it flat out (it was raised by their anxiety). To notice people doesn't actually express the active desire of the flatten out mountain, so is different than using an internal resources for a deed. You can figure out better in this example: as no one remember anymore of that statue, that statue disappear.

VIRTUALITY

The relation between substance, meaning and perception is managed by a material factor. That mean by some condition ("refactoring a code", or maybe "rewriting the book" or "draw something in the dark tower") you can change the universe laws and flat out the mountain.

YOKAI

Everything host a spirit, a mountain is a perfect host for that. Ask the spirit and the mountain can flatten out. Note that's different than magic: spirits aren't a supernatural thing, they are natural part of the world, that reply to this universe ecology. In fact, is a dualistic personification of nature itself (the mountain generate the yokai, the yokai is the mountain, the yokai die and the mountain die).

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Unexplained

"[W]e have a goal to remove a mountain top"

If 'we' is 'us, the authors of this story' or 'us, the out-of-universe creators of this fictional world' then you could simply not explain it at all, just state it.

Fictional example, planet PLATEAU (TAU CETI) from Larry Niven's Known Space. http://larryniven.net/humans.shtml

"This venus-like world would be uninhabitable but for Mt. Lookatthat, which rises out of the soupy, misty atmosphere into a temperate layer, and has a livable surface area on top that's about the size of California." Niven needed a planet like that for his stories, so, it exists.

Real-world example, https://www.alaska.org/detail/flattop-mountain - presumably people can visit it and have "stories" there without knowing how it came to be that shape, or even asking themselves about it.

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Biology / Self-Modifying Organisms

Here's something that's theoretically not impossible even in our universe, and would provide a new paradigm: your universe could contain a species capable of altering its own genetic code just by thinking about it (maybe they have evolved to have an organ which is linked into their nervous system , with the ability to produce arbitrary plasmids and integrate them into the genome of either a) all their cells, or b) their reproductive cells, on the fly). It's not quite technology, as it doesn't involve an external tool, but it's not quite magic either as the symbol/model doesn't bring about the change directly... it just makes the character (or their offspring) able to do whatever it is innately - either through their will, or by hormone changes triggered by emotional states. It also requires more time than either technology or magic, as changing one's body (or reproducing) is inevitably going to take a long time - hours, days, or even weeks, rather than the minutes other methods take - and is probably going to hurt like nothing else!

The flow would look something like this: Volition -> Symbol (Model) -> Metamorphosis/Reproduction -> Profit OR Emotion/Stimuli -> Profit

Eg 1 / Metamorphosis: A character knows they are going into a hostile environment a week in advance, and either [the "automatic" form] a) the fear/stress causes them to grow a thicker skin, strengthen bones, maybe grow a chitinous exoskeleton, or [the "active" form] b) they choose to "build" those modifications into their genetic code, taking a long time to guide their organ to secrete the right plasmids and allow the growth to take place. This could even be risky/disadvantageous to the user, eg: if they do it too much / do it poorly, they could give themselves cancer or horribly disfigure themselves.

Eg 2 / Reproduction: Our character is a hive queen (think ants or bees), and knows their colony is going to be under attack, so they start making more warrior ants/bees or even develop better designs for them - think stronger exoskeletons, stronger toxins, more limbs, etc. Again, this takes a long time, and it's limited to what's biologically possible. Also could be very hard on the user - if they try to reproduce too fast, they might die from the stress!

Hopefully this works - I've never posted on this site before! Sorry if that was disorganized / not quite what you were looking for.

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Frame challenge: there are only rules (which you can exploit with metal tools, living organisms, words and chants, prayers, ta'veren, ...whatever the rules themselves allow), chaos (things happening truly at random), and godhead (the ability to trascend whatever rules there may be).

Technology is about having rules and following them. Science is about finding what the rules seem to be. If the rules to make a feather float include pronouncing "Wingardium Leviosa!" just right, then, however funny, that is nonetheless technology. "Magic" is technology you don't yet understand.

Actually in several novels (e.g. Rick Cook's "Wiz Biz" series, and to a point, Harry Potter and the Methods of Rationality), finding the "rules" behind magic and turning it into tech is the plot.

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Consensus

Convince everybody that the mountain top is gone. Convince them so thoroughly that not even one skeptical soul has the smallest shard of doubt to the truth of the mountain's toplessness. Then, since reality is just a shared illusion supported by the will of the majority, what is believed becomes true.

We couldn't make a machine fly until some brave engineers defied the consensus and through brute force made a new truth and advertised it to the world. Now, somewhere in the world, a 400,000 pound hunk of metal called a 747 takes off every few minutes. Consensus makes the impossible possible. Every stray thought of the mass mind redefines the word "truth".

It's not technology because science doesn't believe in the shared illusion called reality. But it is also not magic, because it makes perfect sense to those who believe it is true. There is no fact, so there is no science... and there is no mystery, so there is no magic.

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  • $\begingroup$ Reality is more than shared illusion. Many brave engineers TRIED to defy the consensus and build a flying machine -- and DIED trying. The Wright Brothers weren't successful because they convinced everyone to change their minds... they convinced folks to change their minds BECAUSE their aircraft worked successfully. And they were SUCCESSFUL because they got the laws of aerodynamics right. Other's machines violated laws their inventors didn't understand. The Wrights built their understanding first, THEN built their aircraft. But "shared perception changing reality" IS a form of magic. $\endgroup$
    – Forbin
    Jul 14 at 19:00
  • $\begingroup$ @Forbin Yes but from everyone's perspective, there is no mountaintop, as like Henry said, they have all been convinced. You're taking the perspective of objectivity which no person has ever experienced anyways. Henry, do you have more on this topic? $\endgroup$
    – Vitulus
    Jul 15 at 0:41
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    $\begingroup$ @Vitulus, only that it was the basis upon which time travel worked in the Christopher Reeve movie, Somewhere In Time. He arranges his environment in such a way that no facet of the modern age is within reach of any of his senses and then hypnotizes himself to have no doubt that he is actually living in the distant past. When he truly believes, it becomes true. I believe this idea is also referred to as the Tinkerbell Effect. $\endgroup$ Jul 15 at 2:10
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    $\begingroup$ @Forbin, please don't confuse my answer with my opinion. I'm not suggesting that consensus has any real power in our real world. I was simply suggesting that in a mythical consensus-driven universe, such manipulation of reality could occur without involving science or magic. Such a world would treat propaganda with the same reverence as fantasy worlds treat arcane lore and science fiction worlds treat technology. Any sufficiently successful propaganda is indistinguishable from magic. As for the absence of a bootstrap, the propaganda which builds the consensus is the bootstrap. $\endgroup$ Sep 16 at 19:32
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    $\begingroup$ BTW, for my "rational limitations" argument I was not talking about any supernatural being who is "only as powerful as her fan base." I am thinking more of Aristotle's concept of a "Prime Mover." Omniscient, omnipresent, and omnipowerful: capable of acting without being acted upon. $\endgroup$
    – Forbin
    Sep 22 at 20:46
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Magic after being explained by science will become technology, what cannot be explained yet will continue to be magic.

Magic trick/ trick

It is magic to the viewer but technology to the performer.

Definition: "Magic trick/ trick" is a means to transform subject's intention to achieve external goal through, at first, creation of internal model (symbol, blueprint), then, after it by the use of an external tool but hide it.

Examples: A murderer who changes tracks at the scene and fabricates evidence for himself; One person wears a bulletproof vest and fakes his death to find the time to counterattack.

Alchemy

Different from alchemy in history, the world we live in is no longer magic. With a world where magic existed and development was on par with technology, imagine how far alchemy could go.

Definition: "Alchemy" is use magic to fortify, enhance, or create materials for technology

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Chemistry

Think of things like acid or fire that do reactions with the mountain until it's gone. Humans can place this there.

Biology

Often helped by chemistry. Organisms use part of the mountain for themselves, or destroy parts of the mountain, to reduce it. Think flesh eating bacteria, but for a mountain. Humans can place the organisms there.

Own power

Everyone a shovel, or use their hands.

Natural

Divert rivers and pool them towards the mountain, using raw water power and erosion.

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  1. Che. volition>meditation> tool>prof Example using che to enhance your strength, stamina and or intelligence

Dreaming. non volition> prof The ability to manipulate reality as if it were a dream However callin be done through the subconscious.

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I would add (1) blind luck, (2) divine intervention (with different flavors: appeal to a deity, intervention of guardian angel, etc.), and (3) "the cavalry showing up". I differentiate the divine from the wizard=magical, and you should do if looking for different alternatives, within a story.

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Coding

My consideration starts from the virtual worlds: from World of Warcraft or MineCraft back to Second Life. In all these worlds many rules are similar to the real world, but other differs quite a lot: you can fly, merge block together to create different objects, travel in many different ways, wear glowing objects, etc. etc.

All these features are not magical, but driven by computer code. You can imagine an universe in which this kind of properties can be created by writing some kind of code from inside the world to create new behaviors that anyone can use.

It's like creating a software plugin for Minecraft that adds dragons to your world.

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Luck

The fundamentals of our world consist of probabilities, which is governed by the theory of quantum mechanics and statistical physics.

Quantum Tunneling

Quantum tunneling is such a phenomenon. The transmission of on object with mass m to travel through a barier with width a is given by:

enter image description here

The inverse of T is the probability. For a 70 kg human to go through a wall that's about 10 cm thick, with a speed of 4 m/s, the probability is e^-10^35. So reaaaally, really tiny. But a person who is "just lucky" can achieve it! This is the link to the calculation: https://twitter.com/i/events/972881765642551297?lang=en

Thermodynamics

Thermodynamical properties are based on statistics. The pressure or the temperature in a room e.g. are determined by the statistical properties of the small particles. Consider two rooms, connected with a small opening. Now, gas particles, out of "luck" could happen to divide in a way that all hot (fast) particles are in the right and all cold (slow) particles are in the left as in the picture below. (I stole the picture from a phenomenon called "Maxwell's Demon", ignore the little demon for this purpose)

enter image description here

This violates the second law of thermodynamics but this scenario could certainly happen with a very, very tiny probability. A person who is just "lucky" could create large temperature and pressure gradients for a short amount of time and could freeze or heat some parts, do explosions etc.

Vacuum Properties

Quantum field theory and thus the description of our particles is a statistical theory too. One popular theory is that our vacuum is situated in a false minimum like so

enter image description here

and could tunnel to the true vacuum at any time with a small probability. This would change everything about our particle interactions and their forces. A mountain could just "disappear" due to a local false vacuum decay.

Also the higgs field may be in a false minimum leading to changed particle masses if it decayed locally suddenly: https://publish.uwo.ca/~csmeenk2/files/FalseVacuum.pdf

Spontaneous Formation (aka Boltzmann brain)

Pair creation (particles creating and annihilating all the time in the vacuum) could lead to complex creations, like a brain (https://en.wikipedia.org/wiki/Boltzmann_brain) with a very, very small probability. Somebody very lucky could create arbitrary structures by annihilating surrounding material. One could annihilate a rock e.g. for something with the same mass, like a human by just "being lucky".

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Your problem is a word.

"Magic" is a term generally used for whatever the story requires that doesn't exist in the real world. Depending on the precise setting, things like the divine, or psychic powers or runesmithing may or may not fall unter "magic". Sometimes they are their own thing, sometimes they are A Kind of Magic (Queen).

So if all you need is something that is "not magic", you can simply define that in your world, psychic powers (or whatever) are distinct from magic.

It is all in the words, really. For example, your definition:

"Magic" is a means to transform subject's intention to achieve external goal through creation and manipulation of internal model (symbol, blueprint), without the use of an external tool.

Actually excludes a lot of real-world magic (we'll ignore the question of it working or not). Many of the western magical traditions, such as the Golden Dawn, do in fact use tools - cups, swords, magic circles, etc.

You could really argue that magic and technology are really the same thing on the meta-physical level - a user's intention is brought into external reality through the use of defined steps.

Also don't forget that until recently, magic and technology were not far apart from each other. The famous Newton, for example, dabbled in not just physics and optics, but also in alchemy.

So if you are looking for a third, fourth, etc. way to "do something" in the world, you need to define the edges of technology and magic. For example, you could simply say technology follows real-world rules of physics. For magic, you would need to define which rules it follows, such as a natural ability of the user plus magical energy ("mana"). Then you could define "divine" as not requiring such an ability and not using mana, but working through prayer and divine influence. Or you could define animism as working not through mana and talent, but through spiritual bonds. And so on and so forth.

tl;dr: you are asking for something "outside" of a thing that doesn't have clearly defined boundaries (magic). That can't work, as any answers are arguable.

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