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In a classic RPG magic system, energy/mana/handwavium points are expended to manipulate reality. The cost increases with the complexity and extent of the alterations being made.

Natural talents for magic are inherent in some individuals, while others rely on magic items. Those without an innate ability can acquire magical skills through decades of training. This question is not about DnD but to avoid questions about "it depends on the magic system, we need more details"

For reference, here's the D&D Spell List.

Given this information and considering that humans have historically had the potential to live over 80 years, even in ancient times, the span of decades, weeks, days, and hours presents ample opportunity for experimentation and innovation.

In a world where individuals can generate lightning bolts from their fingertips, breathe fire, or conjure walls of ice, the question arises: Is it implausible that humans wouldn't quickly invent automation upon the discovery of calculus? Historically, the utilization of natural forces like water, wind, and animals to enhance mechanical processes emerged soon after the invention of the wheel.

Given such a magical world, how swiftly can we anticipate the emergence of the first "computers"?

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    $\begingroup$ Does the magic help keeping away diseases like the plague? Does your world have more or less wars between the 5th and 12th century? If it fares better on both fronts, it could have way more impact than the use of magic. $\endgroup$
    – Mast
    Commented Aug 9, 2023 at 10:24
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    $\begingroup$ According to the OED, calculus is as old as 1672. Parts of it are much older (Archimedes lived somewhere before 200 BC). While calculus helps tremendously with automation, especially the modern kind, it did not kickstart our progress in it. $\endgroup$
    – Mast
    Commented Aug 9, 2023 at 10:28
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    $\begingroup$ Too many variables. Can magic do stuff like calling rain, curing a person, tracking a person, enhancing crops/seeds? If either of this is a yes, then the answer is a yes, provided magic for such things has been discovered in ancient times. Anyway imagine a magic accelerator, aka one-shot rifle that shots arrows? This alone modernizes an ancient man's weaponry to ca.1600 AD level, and this is something an ancient magic user would be able to think of. $\endgroup$
    – Vesper
    Commented Aug 9, 2023 at 12:30
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    $\begingroup$ You are asking about your own world, right, not about the Dungeons & Dragons Forgotten realms (like Baldur's gate games or the Honor among thieves movie) or Solasta's campaign settings? Asking about those is off-topic as it will be asking for 3rd party worlds. Asking for your own world with magic unnaturally similar to D&D's is allowed in comparison. $\endgroup$ Commented Aug 9, 2023 at 13:02
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    $\begingroup$ Niven's Law: "Any sufficiently advanced magic is indistinguishable from technology." $\endgroup$ Commented Aug 9, 2023 at 17:09

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It Depends, But It Might Slow It Down

The thing that advances technology is free time. People living with subsistence farming don't generally have the time or the energy to really innovate.

So the corresponding question for your (not D&Ds, but your) magic system is how broadly available is it? If, like in standard D&D worlds, most people live in something akin to a late Medieval state, and a limited few have access to magic, then I wouldn't expect that to speed technology along at all. That's effectively the state our world was in; a limited few nobles had spare time on account of the feudal system providing for their basic needs. This, incidentally, is more or less how things worked in Pixar's Onward. Magic was hard to do and rare, so it had basically no effect on the development of technology.

If magic is widely available, then what use technology? If you can teleport from point A to point B in a blink of an eye, creating transport more advanced than a horse and cart seems largely pointless. If you can summon bright light to a room with a whispered incantation, gas lamps or a dim lightbulb seem like a step backward. If you can animate a broom to sweep your home, you're not going to be terribly interested in a Roomba. And if you can bind intelligences from other planes into talking mirrors or enchanted rings, you don't really need a Babbage Engine to do your math imperfectly.

If magic is not scarce but still only available to, say, five percent of the population, then there would be impetus in the remaining population to try and duplicate its effects with technology, but there would also be an incentive for that magically-empowered five percent to root out and crush attempts to usurp their power.

Your sweet spot might be if magic made things a bit easier, but only by dint of great effort. A spell that takes an hour to cast powers a millwheel for two hours. This lets magic take the place of animal labour and makes it more available, but provides an impetus for someone to come up with a better solution than hiring a dozen apprentice mages to keep the mill running all day.

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    $\begingroup$ "If magic is widely available, then what use technology?" technology is just widely applied scientific principles. If magic exists, then you'd get magitech. It's not "magic" or "technology" because it doesn't make sense. Tech doesn't arise by itself isolated from everything else in the world. $\endgroup$
    – VLAZ
    Commented Aug 9, 2023 at 5:15
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    $\begingroup$ @VLAZ - that assumes that magic can have scientific principles applied to it. As I've said on other questions of this sort, if we assume the entity that is "magic" actively works against the codification of magic, by altering its principles, making it more dependent on the user, or responding punitively to any attempt to better grok it, then no, you won't get magitech, because the scientific method will not apply. $\endgroup$
    – jdunlop
    Commented Aug 9, 2023 at 8:00
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    $\begingroup$ Are you're saying there are a lot of assumptions you made as part of your answer, thus it doesn't really hold up without them? Also, if your assumption is that magic defies consistent usage, then how does your statement "If you can animate a broom to sweep your home, you're not going to be terribly interested in a Roomba." make sense? With the premise of magic being unreliable, you wouldn't be able to consistently have an obedient broom sweeping your home. Seems like just in that situation, if someone were to offer you a Roomba, it'd be an improvement. $\endgroup$
    – VLAZ
    Commented Aug 9, 2023 at 8:07
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    $\begingroup$ @VLAZ If you can easily rely on magic, there's less incentive to put hard work in science and technology. Different forms of technology would arise, like magitech, but the assumption the speed of discovery would slow down relative to non-magic is not a bad one. $\endgroup$
    – Mast
    Commented Aug 9, 2023 at 10:20
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    $\begingroup$ @Mast my point is that "technology" is not some thing that's entirely divorced of context. If people could shoot fire from their fingertips, we'd have technology that works with this. Technology is not defined as "applied science but without relying on fire from fingertips". We do not have fiery fingertip technology only because of lack of fire coming from that part of our bodies. If you have reliable magic, then you'd have a technology developing in lockstep with it and based on it. If magic is unreliable/uncontrollable, you'd probably get something different. $\endgroup$
    – VLAZ
    Commented Aug 9, 2023 at 11:28
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It's entirely up to you!

From the Yes view.

From a straight-faced assessment of the question, my answer would be yes. The Unseen University in Pratchett's Discworld novels seems to have a flavour of this, especially considering as it's home to the Discworld's first computer, Hex.

Being able to conjure golems to crank machines anywhere? Or just enchant the machine to be self-powering? Yup, that will absolutely rule. Arguably, you could extend a lot of this thinking. Magical horse drawn cart? In a few years you've got a Ferrari. Fireballs and magical shields? Put some uranium in the middle of that sucker and you've got a nuke.

The possibilities are endless with a bit of imagination.

From the No view.

But, you don't have to do that. A wonderful version of this I saw was in the great game, Arcanum: Of Steamworks and Magick Obscura. This game's world had the principle that tech and magic were fundamentally opposed principles, on a cosmic scale.

Your character had a magic/tech alignment as well as a good/evil alignment. The more you invested in magic, the worse you got at tech, and vice versa.

In addition, the two principles opposed one another in the day-to-day world. Bring a mage into a busy industrial city, and watch his fireballs flicker into zippo flames, or even fizzle or malfunction altogether, sometimes to disastrous effect. The cloying presence of tech and physical materialism suppresses the powers of magick.

Meanwhile, try and run a train through an elven forest, and gears would grind, hydraulics would block and freeze, and entire engines would fall to pieces to rust in the jungle. The mere presence of a magickal field is subversive to the common laws of nature and physics, so things built on those principles founder.

Sidenote: Sociopolitics

In Arcanum, this had some really interesting socio-political implications too. Elves in cities often find themselves ghettoized, as their presence near the busy industrial hubs is bad for business; maintenance costs rack up. And they're not much good working in such an industry either.

Likewise, elven strongholds and wildlands would become fiercely xenophobic, fearful that the encroachment of, essentially, technological gentrification, would stifle their powers, freedom and culture. Engines? Not in our back yard!

Conclusion

You've got a mountain of options here. Find which one appeals to you best, and consider the implications of that system with a little imagination. Good luck!

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  • $\begingroup$ I agree and the "yes" view is a good lead in. Reminds me of a recent question about a world where everyone can cast "Spark". You can skip decades of bullet development by simply not needing to invent a primer if everyone can spark their own bullets. Perhaps advanced automated factories are invented far earlier, because they are built by necromancers using skeleton workforces for the "automation". Just need enough imagination to figure how modern devices might be done easier/earlier with magic filling some of the tech gaps. (Nanochip manufacture easily handled by nanodwarves.) $\endgroup$
    – JamieB
    Commented Aug 9, 2023 at 15:38
  • $\begingroup$ You know when you DL from GoG and there's ads for other games? This is one of 'em, and it's what you should've if you didn't. Tim Cain et al, of Interplay's Fallout, became Troika Games when they left Black Isle. $\endgroup$
    – Mazura
    Commented Aug 9, 2023 at 20:32
  • $\begingroup$ "the principle that tech and magic were fundamentally opposed principles". Isn't that a pretty common (or at least formerly common) trope? $\endgroup$
    – RonJohn
    Commented Aug 11, 2023 at 14:57
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Both Yes and No

In some ways, magic might speed up development to a higher standard of living and advance technological development. In others, the availability of magic might make technology obsolete and reduce the need for development there.

Let's make some basic estimations that crucially impact the effects of magic on tech development.

Magic is omnipresent and omnipotent!

If magic is so abundant and powerful that anyone can just summon a knife or food, there will be no technology. There is no need for any technology with magic so accessible as magic is doing everything.

Magic is extremely rare

On the other end of the spectrum, magic might be so rare that to even see a true magic wielder would be a once-in-a-lifetime event for most people living in an urban center. Only one step further on this axis would be there is no magic. As a result of how rare magic is, there is only a very limited impact of magic on technology.

Magic is just rare

Now, in the middle ground, magic and technology will have influences on one another heavily. As pointed out above, magic needs to be somewhat accessible to even have an impact, and then it depends on the ease of the magic.

Let's take some examples of how magic may impact technology:

Lighting

If there is a way to illuminate spaces cheaply and easily, it is preferred to other ways. An ever-burning lamp might make any other lamp obsolete if it is cheap enough and thus might reduce research into other ways to illuminate, such as electricity.

Cooking

A lot of technological development starts in the kitchen. If magic can make kitchen work easier or open new ways to cook food and drink, it will have a massive impact here. For a simple example, think of a spell that finely minces meat - that might create food more akin to modern fast, such as fine sausages. Spells that dry food might lessen the impact of bad weather, and spells that help in refrigeration likewise.

Now comes the kicker: If magic is not abundant enough that everybody can afford it but abundant enough that everybody knows about the effects, smart people will try to replicate the magic effects or reduce the complexity of magic required and get done as much as possible with the lowest magic effects possible. As a result, you might gain a lot of hybrid Magotech.

For a random example, maybe it's a fridge that uses a single enchanted gear to drive a fan in the ice box and an enchanted rock that always is at freezing temperature as a cooling device.

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Necessity is the mother of invention

I was going to simply agree with @jdunlop but I disagree with his/her reasoning à la free time. Magic is an alternative to invention, and in old times, invention was considered to be magic for its ability to expedite tasks. Humans are a society governed by the same economy imposed on us by our nature, being a species limited to a number of years as you put it.

If society had two solutions to a given problem, such as shooting an enemy with a weapon; the one involving a great deal of time, money, and invention, such as producing a gun to fire a slug of metal at a high speed; and the other being some incantation that launches a bolt of lightning from your hand in a direction of your choice, the effort to construct a gun might simply never be put in. Why would we? Ultimately, the decision of whether to use a magical ability or a technological solution will depend on a number of factors, including the cost, reliability, and versatility of each option. However, in general, because the cost of a magical solution is effectively zero by definition, the discovery of a magical ability is likely to lead to a decrease in the pace of technological advancement in that task area.

Why do I say the cost is zero? Because in a causal universe governed by physics and laws of conservation, the cost of any activity is balanced across the almighty equality sign. Nature and her forces are defined by that single ability to make both sides balance out, such that nothing is ever created nor destroyed throughout any causal relationship. Magic, on the other hand, is a supernatural concept which ignores this balancing act. Of the various definitions available they all follow that theme.

Collins states it succinctly:

Magic: n. The power to use supernatural forces to make impossible things happen, such as making people disappear or controlling events in nature.

The key word here is super, which implies that it is outside of nature's explanations. It can't be achieved through natural events, and is thus outside the purview of science.

Computers

Since the OP asks specifically on this point, a world which could scry answers from crystal balls or divine them from a Tarot deck reliably would certainly not invest billions of dollars into developing power hungry computer chips, Internets, or artificial intelligence.

If oracles could ask their gods for answers to future events, there would simply never be any stock exchange, no investors to pour money into new electric vehicles, and no news reports of economic fluctuations. If humans could teleport, there would be no investment into security devices or doorbell cameras or cell phone tracking. What would be the point of it?

  • Bob: "Hey, I have an idea! What if we could see who's at our door even when we're out shopping? I can invent a camera that uses radio waves to chop a picture into little bits, transmit them over some huge towers powered by electricity so I can put them together on a radio telephone and see the picture anywhere I am! Wouldn't that be great?"
  • Sam: "You still use a door? Seriously? I just spoke to my kids at school and they reminded me, I thought we were going fishing this weekend? You going to spend all your time on that stupid workbench now?" saying this as he puts his miniature crystal ball back in his pocket.

It is not just the availability of free time that allows for technology, people will not invest their time or effort into efforts that simply do not meet any need. Since magic accomplishes impossible tasks, it removes the very need for technology in the areas it works. If your world has magical flight or levitation, they will not build airplanes unless the flight is somehow limited to very slow speeds. Likewise for teleportation. If your world has premonition, oracles, precognition, or future sight, then neither stock markets nor computers will likely ever arrive. Without stock markets most inventions will never get funding, and technology will come to a halt. If your world has magical projectiles or lightning bolt type weapons that don't need any gun-like device, then ballistic weapons won't ever be invented.

Because magic circumvents the resources required to invent technology, it is superior to technology in filling any needs for the areas that it operates. Therefore, magic will logically slow technological advances in all areas where it overlaps with technology.

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  • $\begingroup$ Up to you, but I'd recommend taking your last sentence (which I agree with) and also insert it at the beginning of your post. Sort of a 'bottom line up front' presentation of your answer. $\endgroup$ Commented Aug 9, 2023 at 15:37
  • $\begingroup$ Reliable prediction, such as oracles, wouldn't eliminate the stock market, but only make it more reliable. Recall the market is actually just a way to crowdsource venture capital. Rather than predict which stock will rise the most, look into your crystal ball to see how much a company is worth in your time horizon. Everyone else is. $\endgroup$ Commented Aug 16, 2023 at 13:21
  • $\begingroup$ @MichaelFoster It would be impossible to have a fair market unless every potential investor had equal access. If knowing a company’s intent is inside information, then A crystal ball is automatically “inside information” of the worst kind. No government could regulate an exchange that already knows its own performance. That actually creates the bootstrap paradox. $\endgroup$
    – Vogon Poet
    Commented Aug 16, 2023 at 15:20
  • $\begingroup$ @VogonPoet One can forget that the purpose of the stock market is investing, not speculation. The crystal ball should be used to find when (due to one's need for the money) one should sell, and what the company's value would be at that point. Others would make similar assessments. The only difficulty would be unscrupulous people telling others false future readings, when those people can't afford real ones, and so getting them to buy or sell for an incorrect price. But the actual market would have real data which could be independently verified. $\endgroup$ Commented Aug 16, 2023 at 17:56
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I think that everyone would agree that "It Depends". It depends on the specifics of your magic system, on how flexible it is and what it allows its users to achieve.

If your end goal is computers, then you'll need to examine your magic system and see if you can get there from that starting point.

The D&D spell list is a fixed list of spells with quite specific utility, and it does not encourage magicians to engage in materials science, nor is the spell list easily expanded.

At best, a D&D magician might be able to summon some being that can think for them, or build automata that can form the logic elements of a basic computer, but in general, the magic system seems to focus on combat rather than innovation.

So, it seems that for D&D, the magic system is more of a hindrance than being helpful for the goal of designing and building computers.

This is not to say that a different magic system would have a similar effect. The Ars Magica magic system is deliberately far more flexible, and could conceivably contribute to magic-based rather than electronic computers in a future based on it.

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Magic is capable of creating slaves, aka golemns, deamons etc. Slaves definatly put a price cap on technology. Below the cost of feeding a human beeing no tech shall walk the earth.

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I think nice way to think about it is in terms of supply and demand, and then decide where on the spectrum does your world lands.

How does magic change the supply of technology and demand for technology? Supply of technology, does magic in any shape or form make the process of inventing new technologies more costly? I would say no, opposite in fact. Any budding inventor, can make use of magic to simplify his research. Magic makes it easier to acquire resources, to conduct experiments to do science. Imagine Galileo Galilei having access to Fabricate spell, he could transmute glass in much bigger lenses and make more detailed observations of the night sky. I vote that magic would act as a boon to supply of technology. Even the simple send Sending spell would allow faster and therefore productive communication between scientists.

Now the other side, the supply. He it would have negative effect. We want technology because it makes our life easier, allowing us to get more, for less. In fantasy world, there are two ways to achieve this, via technology or via magic, since technology does not have monopoly on the quality of live, I would expect the demand for technology to be slightly lower. But (and that is a big but), in most fantasy settings I have seen, the magic is just not an abundant resource and (in general) suffers from immovably limited supply (call it quota). And this quota gets devastatingly high with more complex magical spells. Technology, while also at some point hits the laws of conservation of energy, for most parts, will far outstrip the limitations of magic. Meaning that while at the beginning the drop of demand may be substantial as the cost of alternative is relatively low. When we get to great feats of technology, only limited number of magic user will be able (not to mention willing) to compete. And the demand for technology will therefore experience only slight decrease, while the supply will still be similar.

So how quickly can we expect the emergence of first computers? I conclude that sooner than in the non magic world. How sooner? Depending on how accessible is technology to general population, ie. how much does magic compete with technology given free market conditions.

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I would take from the adage. "Necessity is the mother of invention". When the NEED is greater this incentivized innovation. With magic present it may retard the need, or divert the efforts to innovate toward focusing magic to fill needs instead of forging new paths into conventional technology.

Why waste time and effort hauling water and building that clunky contraption to wash your pants when you can just use a basic Clean Cantrip?

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In a world like that, magic might just be another branch of technology.

In a world where individuals can generate lightning bolts from their fingertips, breathe fire, or conjure walls of ice, the question arises: Is it implausible that humans wouldn't quickly invent automation upon the discovery of calculus? Historically, the utilization of natural forces like water, wind, and animals to enhance mechanical processes emerged soon after the invention of the wheel.

Not necessarily. Automation is convenient, and someone would have had to discover how to conjure walls of fire-breath from their fingertips in the first place. In a fair few settings, magic isn't innate, and must be learned, or trained.

All you really need to get started is for someone to think that there might be a better way of creating a tapestry, and set about creating a magical loom that can do the work of 10 weavers.

It's not far-fetched for a magical setting to use magic as a power source, in lieu of natural processes. You can build a windmill anywhere if you can summon the wind on demand.

Given such a magical world, how swiftly can we anticipate the emergence of the first "computers"?

Insufficient information for a meaningful answer. But computers today arose from the extensions of calculators, which a magical world would still need for trade and business. That need doesn't really change in the presence of magic, unless there's a "calculate this for me" spell (but that's a calculator in and of itself).

Although it is worth noting that part of what spurred the development of modern computers was the world wars. They had existed before that, but that was what really helped kicked off modern computing.

A magical world might not go down that angle, which might make computers happen later, or not happen at all.

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When we study ancient history, one of the things that we realize is that people won't adopt innovation unless they, personally, feel the need. Let's take writing as an example.

Writing, in any culture, developed as a side-effect of social clustering. When the number of people exceeds the Dunbar Number, a ruling class will form. The ruling class will need to collect taxes, and writing is developed as a method for tracking tax collection. It's well known that computers were first developed for gaming, but math was developed for taxes.

Skills are a little different. If someone can practice something in private, then it doesn't need a reason. Acrobatics was invented so many times that it isn't even worth keeping track of. That's how alchemy advanced. It's also why alchemy took so long to turn into chemistry. You can't readily pass skills around.

Sufficiently Advanced Magic

This is the boundary between capability and technology. When you can do something, it's a capability. When you can provide someone with an artifact that allows anyone to do something, it is a technology. If it's a capability, then it won't be spread around. If you can make magic items, then it will become part of the world's technological heritage. This is the "Sufficiently Advanced Magic" dynamic that I explore in "The Thaumechanical Man."

It's inevitable that the creation of "magic items" would become an industry. It's further inevitable that magic items would be used in industry. They would develop "stone to mud" and "mud to stone" as a standard construction technique. Tensor's Floating Disk would be standard equipment in every warehouse.

Like our computers, this dynamic would increase the average productivity of humanity. Just like every other technological advancement that increased idle hours, it would not just advance innovation, but increase how widely and cheaply new innovations could be reproduced as technology. Magic would BECOME a form of technology.

Interference patterns

In the D&D universe, there is no inherent conflict between magic and technology. There's no reason why a gun might not use a mechanical feed mechanism and a magical propulsion method in the same device. In some universes, having magic near your technology has a habit of warping the rules that the technology relies upon.

This is where "it depends" comes in. Experimenters would spend a lot of time trying to figure out how close they can bring a set of gears to a water elemental before the gears warp and fail. By definition, the phenomena would either be deterministic or probabilistic, and researchers would identify those parameters. In our reality, we've reduced everything to determinism except for quantum actions and, Copenhagen Interpretation aside, we aren't sure about that one, either.

This "separation factor" would be the primary characteristic you'd have to specify to determine if tech and magic could be used together in your world.

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I'm not going to ask about the details of the magic system, but I am going to make two very broad assumptions:

  1. The physical laws of the universe are relatively stable except when being actively messed with.
  2. The ability to use powerful magic and/or create enchanted items is relatively rare - less than one in a thousand can do more than cantrips for instance.

Under those conditions it seems likely that the development of technology would be fairly inevitable, because a non-magical solution is available to more people than a purely magical one. Yes, the very rich can afford stables of mages and expensive enchanted items, but even the moderately wealthy will rely on non-magical means most of the time due to the inherent cost of magical items.

Anyone who's ever tried to buy a very simple magic weapon knows that the prices scale pretty darned quick. My new adventurer can pick up a normal sword for around 10gp, but even a measly +1 magic sword is going to cost me at least 100gp - in terrible condition, with none of the flash and style we all love so much - and maybe as much as 500gp. Or more if I'm gullible. And don't even get me started on magic armor.

And it only gets worse when you want something useful outside of battle. Why spend a few thousand gold for an enchanted item that you can ride like a horse but only outside of battle when you could simply buy a horse for a tiny fraction of the price. Could I create a kitchen mixer that runs off magic? Probably, but it's going to be a hell of a lot cheaper to beat those eggs by hand, you know? Not to mention that so many powerful magic items - especially the utility ones - have long recharge times. Sure, having a figurine that can transform into a Nightmare for a day (for the low, low price of ~128K gp) is cool, but you can only use it once every 6 days or so.

So... what do the common people get? Normal, everyday tools and weapons and animals. They hitch their wagons to actual horses or oxen, just like they did in our own pre-industrial world. Nobody uses magic to plow fields - well, except maybe the elves, but who knows with those guys.

But it's not just the non-magical peoples we should look to. How about the large portion of the magically-enabled community who never manage to get beyond simple cantrips? Not everyone is an arch-mage, or even a 10th level adventurer. Most of them are essentially commoners with one or two little tricks they can do that don't actually help them all that much. But you know what? Control Flames is really useful in a kitchen or a forge, and from the description I'd be willing to bet it would be damned handy for someone doing welding.

All of which are good reasons why people might want to invest in technology when they have time to do so. You know, when the whole continent isn't being attacked by undead or monsters from the underdark or what have you. Normal people doing normal things with normal non-magical tools are good at coming up with ways to make their own lives easier, or to reduce the cost of manufacturing or whatever.

Or you could use goblins as a slave race or something. That'd probably set your progress back about 100 years.

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Everything will be completely different

Just to add to the "It's up to you" answers. Remember that as soon as you step out of our world, into a world with a different history, technology advancement will most likely be different anyway, and I don't just mean the speed at which it develops. Different geography and historical events will lead to different inventions.

And that is even before you add in magic. Once you do that, it completely mixes it up.

The potential differences are widespread. But for example, no world wars likely means less advancement in aeroplanes, but that's probably OK because we probably easily make airships float without the need for filling them with dangerous hydrogen - or even teleport. The ability to create, say Golems, and now you've got the house-keeping robots with advanced AI the people in the 60s dreamt we'd be using nowadays, but long before even a computer was invented. Every new spell you add in completely changes things around again.

By the time you get to your chosen point in history, the technological world will be unrecognisable from anything we've experienced on Earth.

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Another perspective that might tie into some of the other answers is to think about how science leads to technological advancements. Usually, it's a very iterative process with small gains where we learn something new, which in turn lets us create marginally better tools, making it possible to learn a little more, etc. If magic allows us to skip over 50 years of intense research to achieve some kind of result while ignoring the details of some underlying process, then to catch up, we might have to go back to 50-year-old technology and start building from there. The problem is, who wants to invest time, effort, and money to live in the past for the next 50 years? So what could happen is instead of 50 years of intense research, we now have low-investment or hobby research that might catch up in 100+ years.

With that said, magic might benefit certain aspects of the research process. For example, if it can be used to generate cheap energy, then research budgets can shift money from power costs to other things, like more staff. There are a lot of potential scenarios depending on the magical system and how it's applied. So it's possible that maybe some technological advancements would benefit, and others might be held back.

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Science and Measurement Tools

Often in the history of science new discoveries are the result of new tools being invented to measure the results of experiments. See for example the early tools to measure the speed of light. A whole new set of capabilities provided by magic would probably make many science experiments easier to conduct. So even if magic isn't guaranteed to speed up technological development in all scenarios, it stands a vey good chance of speeding up scientific understanding just like technology does.

The Divination Gotcha

If your wizards concentrate too much on answering questions about the world by divining the answers from sources that don't themselves actually know, or who lack the language to express the answers. Like asking spirits or the collective unconscious about the microscopic world. Then it's easy to get into a situation where no new knowledge is ever discovered outside the existing view of the world.

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