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So lets say that the level of the non-magic wielding species i.e. humans technology is at around the level it was in the early medieval times.

I would then introduce magic to the rest of the world in a form of a new species. The species i.e. elves would have lived within the world but hidden from the humankind. They would have long traditions with magic etc. The whole race would be peaceful (with a few exceptions).

The magic would lurk in to the world as humanity knows it, through some elves sent to live among them. And the country/ area of elves would become open for trade etc. (All of this due to the elves needing more resources etc. to live in the small area with a growing population)

There would be a few very strong elves who wouldn't have many limits on the magic, but those few would have more like a god status and have little to no interest in the happenings of this world.

Then there would be also a few powerful elves whose magic is strong enough to be the leaders of the elf country. They'd be peaceful and only use their powers when needed to defend their kind. If there was a war they would be easily the most powerful country in the world.

The average towns folk elf would be powerful compared to humans, but they wouldn't have so many spells or types of magic they can control. I.e. one could hold about 5 different spells which would be directed toward their professions and learned with long training. So lets say there was a farmer elf. That elf would probably have spells related to water, growing plants, shaping of land and around two others. On top of the main spells they would have learned a lot of weak spells etc.

Wielding magic without any magical items would still be very rare in the human countries and the average human could only learn to wield it through certain life threatening rituals and years of studying and training.

There would however, be many magic items introduced to humans trough the trade some countries open with the elves i.e. potions, weapons and lets say crystals that hold magical energy (would be needed to use magical weapons) and many other types of things. These items would be "low in magic" making the elves and few people have the real power of magic.

Magic would (very) slowly become inherited(?) to the mankind through slow mixing of the species (which would be banned at places -> very slow). It would however make the powerful magic wielders increase with time.

Problem comes with the few master crafts elves and weapon makers etc. who'd be able to make guns or something like that. And these could "modernize the world overnight" so to say.

The problem what this makes, is that (what I call) the technology level of the world would eventually increase its developing speed when I want to keep the human side of worlds era in the middle-ages (and generally not modernized) as long or possibly longer than it was in the Earth.

I really don't want the world to get to modernity any time soon, so my question is:

How do I keep the (mainly human) world from starting to develop their technology level too fast or "modernizing overnight" with the introduction of magic?

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In my opinion, the presence of magic would have exactly the effect you are looking for; slowing down the advance of science by both interfering with the scientific method and by destroying people's motivation to find hard science-based solutions when easy magic-based solutions already exist.

This was explored pretty thoroughly in this question, which I posted a while back.

To sum up the major ideas...

1). Science relies on the repeat-ability of results under experimental conditions. From this consistency, we draw theories which slowly grow more trusted with every successful repetition. Eventually, theories which have shown high reliability become a solid basis of further exploration which leads to new discoveries, new theories and a continuing cycle of knowledge growth. A single failure to repeat invalidates a theory, forcing us to find new explanations for what has occurred. ...unless magic is an option. Once magic is available, no revealing failure can be trusted, no experiment can be guaranteed to be free of magic tampering. The mere existence of magic undermines the scientific method. Without the significance of repeat-ability, which magic destroys, scientific growth flounders.

2). Science relies on real-life needs to motivate the arduous experimentation and repetition which leads to growth. When magical solutions exist for those real-life needs, the motivation falters, and scientists find other ways to spend their time. Nobody chooses the hard road when an easier road is also provided.

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    $\begingroup$ This is an interesting answer but I think OP means problems solved by magic as technology level, not just technology based on sciences. $\endgroup$ – Real Subtle Oct 13 '18 at 8:31
  • $\begingroup$ I can't help noting that the the substantial majority of the answers to your linked question (including the answer you accepted) boil down to "Yes! Science would still exist, and be useful, even in the presence of magic." This completely contradicts your point 1, while your point 2 is entirely dependent on the assumption that magic is easier than science, which is very setting-dependent. $\endgroup$ – Dave Sherohman Oct 13 '18 at 9:26
  • $\begingroup$ @DaveSherohman, good points. I remember that the answers I received were a little surprising and even convinced me for a time that my assumptions were wrong. Strangely enough, in one of my works in progress which is now over 4 years in the making, the central theme is still more aligned with my statements above than with the answers I received that day. My goal in posting this answer was to help. If I contradicted myself a little in the process, I hope that doesn't get in the way of it being helpful. $\endgroup$ – Henry Taylor Oct 13 '18 at 15:46
  • $\begingroup$ @RealSubtle, so you are saying that the OP's world getting to modernity through magic in the absence of science is what we want to avoid; avoiding things like having battery powered radios even if the batteries are replaced by magic crystals and the radio waves by telepathic connections. You are correct that my answer didn't address that challenge. Hopefully some of the other answers will. $\endgroup$ – Henry Taylor Oct 13 '18 at 15:56
  • $\begingroup$ @HenryTaylor this paragraph of the question: "Problem comes with the few master crafts elves and weapon makers etc. who'd be able to make guns or something like that. And these could "modernize the world overnight" so to say." suggested to me that was what OP meant. $\endgroup$ – Real Subtle Oct 15 '18 at 7:51
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Have incompatibilities between magic and large-scale (or often repeated) operations.

In our world, the increase in the rate of technological progress from 1700 to 1970 was closely associated with the accumulation of physical capital. Each new technology could be used to improve a larger amount of stuff than was available to the previous technology. Many of the new technologies only made sense in the context of "factories", "pipelines", and "industries".

If magic is inherently a "craft" that can only work on a few small things at a time, then the feedback loop will not get out of control.

For example, make magic increase inter-personal conflict.

If it is hard to have many people work together in a magical environment, magical factories and universities will not be practical. This will prevent the feedback loop. It also explains why so many plots (that are interesting to the author) involve magic.

Another example is to have magic users get bored easily, so they don't like repetitive work.

Or make magic work better in societies with very high marginal tax rates / very low savings rates.

Communism does not work in non-magical societies. But what if magic can make communism work well enough? Communism's high marginal tax rates will inhibit capital growth, and thus slow down the feedback loop.

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    $\begingroup$ Aren't you mixing up communism with social democracy? Under communism there was actually tendency to invest higher share of GDP than under capitalism. Just the investments were done by gov so you may guess efficiency. $\endgroup$ – Shadow1024 Oct 13 '18 at 15:40
  • $\begingroup$ @Shadow1024 -- You make good points. As you mention, the "efficiency" is such that 15 years into Russian, Chinese, and Venezuelan Communism, there was widespread famine. And Cuba caps most people's monetized income at 20 dollars per month. This is effectively a 100% marginal tax rate. $\endgroup$ – Jasper Oct 13 '18 at 18:54
  • $\begingroup$ @Shadow1024 -- More to the point, central-planning models of Communism are designed to prevent the exponential growth of small businesses. (The model instead tries to build a few large businesses, which can be more easily controlled and measured.) The unpredictability of which small businesses will grow the most is closely related to the technology/capital growth feedback loop. $\endgroup$ – Jasper Oct 13 '18 at 19:07
  • $\begingroup$ Central planners' "need" to minimize variability in both supply and demand, at both the small-scale and the large-scale, will cause a Communist government to be in conflict with local and independent magicians. Especially with magicians who do practical things. This is in addition to the conflicts that we see in the non-magical world between most Communist parties and religious leaders. Like magicians, religious leaders claim that there is more to life than just scientific phenomena. $\endgroup$ – Jasper Oct 13 '18 at 19:45
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    $\begingroup$ Actually wizards would be ideological nightmare on a few levels. Not only the supernatural stuff, but even worse with hard evidence. Nevertheless there is an extra feature - magic is terribly anti-egalitarian. The means of production... of witchcraft are by default spread in a terribly unequal fashion are not subject to any redistribution. $\endgroup$ – Shadow1024 Oct 14 '18 at 16:00
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You could introduce some constraints.

  1. The use of magical weapons and hand-held objects requires magic. The use of magical installations (i.e. magical dam or plumbing or whatever else) requires magic drawn from the Earth, which is not limitless, at least not without digging very deep down. And it also frequent maintenance by magical specialists.

  2. Humans and elves are two different species, and while they can interbreed, their offspring will be infertile and will not have children to inherit their genetics. (i.e. horse+donkey--> mule)

  3. Alternatively, humans and elves can only reproduce together with the help of magic: this magic also requires a qualified elven doctor/midwife/whatever you want to call it.

  4. The only ones who can make magical objects are ones who can wield magic, i.e. elves or hybrids. They prefer to live near nature, so they dislike working in cities. Which means people living in small villages might have more technically advanced living conditions, which in turn might put a stop to the spread of large cities and keep people living in villages. On the other hand, it might mean that people who have to live in cities would develop technology based on science and not magic. This would be an interesting concept to explore, I think.

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Technology's impact is felt more because it can happen on a mass scale, not a small one. We've uncovered things in archeological digs that are more advanced than the current tech for the time period was--like a calculator from a Greek shipwreck. Just because it exists doesn't mean it will spread--if it's hard or too expensive to make, or doesn't seem to have a practical purpose.

You already have limitations in place. And those limitations make magical tech RARE, and therefore expensive and not available to all.

Most magic users only have 5 spells per day, and most of what they can do isn't something that can benefit non-magical users.

Secondly, you're talking about magical guns, but I'm going to talk about magical BULLETS. So maybe you have a few magic makers who make guns. But those guns need a supply of bullets--and a gun becomes useless without them without a regular supply.

Third, if no one outside the makers understand how to make the guns and the bullets, then THE MAKERS are the resource. It's like if you introduced a gun to the Romans. They might be able to fire it, they might even understand it's metal, but they wouldn't know how to refine that metal and make a proper barrel good enough to get the same effect. And they wouldn't understand how the bullets were made either.

Fourth, you can create a guild that limits most of the "tech" to one-off or one use items. So a crystal or something can have the power to do something, or a potion might heal ONCE, but that's it, and it's expensive.

Fifth, you look at mixing as a way to up the magic in the whole of the population, but...maybe it's also a way to siphon off magic from the elven population. This can happen one of two ways. The first way would be that magical energy on a planet is a finite resource contained within PEOPLE, specifically magic users. The more magic users there are, the less magic there is to go around. Way two is that magical aptitude is found genetically within elven genes only, and if you actually quickly mix the two races (instead of slowly) then the big magic allowed gets less and less, while the little magic will be fairly common (because everyone is mixed). For the purist elves, if they are staying within their race only, because the mixing is widespread, it's difficult for them to find pure-breed elves to breed with. This means inbreeding, which can come with a host of genetic disorders, death, insanity and so on.

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