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The main character died, and they are transported into another world. Before they are sent by the deity to the other world, he is given overpowered skills. The main character is also given a game-like functions like map, inventory, and status.

The world is mostly in the medieval period, the country that the main character lands in is also in the medieval period, socially and technologically. This world also has magic.

Magics here are like a computer programs that affect the physical world. They can also be treated as functions which you can combine together into a bigger magic. Particularly high levelled magicians can make magic by imagining, but magic created this way consumes way more mana.

The main character can freely make magic using both methods.

How long will advancing a medieval period country to a spacefaring intergalactic country take for the main character in terms of years, given other aspects of society other than the technological aspect?

EDIT:

In response to the comments, I’m sorry for not giving much details, but I will clarify, and add other additional information that I didn’t think to include.

The two main skills the main character is given are Increased Growth Rate and Absolute Disassembly.

Increased Growth Rate overrides the main character’s experiences gain increase to increasing strictly at an exponential rate for every kill he does. The experience required is always 1 EXP.

Absolute Disassembly disregards the drop tables of monsters and makes it so they always drop their rarest drops and maximum amount of money regardless of the LUK stat of the person.

Additionaly skills the main character got are search, analyze, map, inventory, and status, all put neatly organized into a menu.

They also gets their smartphone that is now connected to the Library of Alchias, which is a library with all of the knowledge in all of the multiverse. Of course with the infinite vastness of the multiverse, The Library of Alchias is set to displaying information gotten from Earth and Satna’andaz (the name of the world the main character is sent to), and current world. The information available includes all of physics and the human made mathematics for it, all of the knowledge humankind of Earth and Satna’andaz, and all of the things humans do not know. It is also wirelessly conntected to a headset with headphones and visor.

They also gets an AI companion that is now residing in their smartphone. The AI can access all of the functions of the smartphone, including the Library of Alchias, and the main character’s menu.

The their phone is also going to be the living space of the deities they will ‘collect’ across their journey in Satna’andaz.

Early on, the main character learnt Instant Learning and Eidetic Memory skills, so he can understand and memorize even the most advanced of physics equations even if they have only seen it for the first time. The main character also instantly learns (but not masters) skills by doing them once, but thet do not master them instantly.

Every level up, the main character gets magicraft points, which they can use to level up skills. Skills can be mastered two ways: by repeatedly doung them, or by spending magicraft points on them.

For beginners, magic is invoked by imagining the phenomena, chanting the associated spell, and pointing a wand at the target, for master magicians, they can invoke magic without doing any of those. A simple Move magic that moves objects over a distance over some speed takes 1 mana/kg*m/sec A CreateTower magic that creates a typical 10 story building takes about 1, 000, 000 mana if the magic is created using imagination, if the magic is created by composition, the cost depends on how efficient other magics are used to compose this magic, at best it can be 1, 000 mana. But making an X-fighter type spacecraft with FTL capadpbilities is relatively easy if the magician has appropriate knowledge of General Relativity, and other related fields of physics. Magic can be used to break the laws of physics, but the mana cost becomes impossible to overcome. It also allows people to go from one universe to the other, given enough mana.

Magic can be casted and enchanted to objects. The difference is that casting just makes it so that the magic is toggleable, and requires active activation by the user, enchanting is where the magic is always on, until the source of mana (usually the user) is removed or depleted. Magic that can be casted or enchanted to objects are dependent on the object, i.e. one cannot cast FireProjectile to a sword, unless the blade is detachable. Activation of the magic casted or enchanted to objects requires the same amount as invoking it directly. There is a magic called Program, where one can program the functions of the object, and make the magic casted or enchanted to the object interact with one another. Program can also instruct an object to do things within their capabilities, i.e. objects that have no wings or do not have Fly enchanted on them cannot be instructed to fly.

Mana replenishes naturally by the body. Anything with life can generate and replenish mana. The rate is dependent on the INT stat, the higher it is, the more mana one has, the faster it replenishes. Magic is usable by any life form. However, magicians in society are trained elites. They require heavy testing for licensure before being able to take societal jobs, like healing and construction. Tests include theoretical and practical. Being elites, magicians are highly sought after, and the pay is high. The creates animosity with people that cannot use magic to solve the problems in various fields. Anyone can use magic, but not everyone can become a magician. Adventurers also can use magic, but only in dungeons for their livelihood. Adventurers do not have as strict of a licensure test. Anyone can become one.

The main character’s goal is to make magic tools that anyone can use regardless of training and mana availability, and disseminate them throughout the country and then the world. They do so by enchanting and casting magic to objects, and making a a source of mana that contains enough to power the tool reliably for a long time.

Creating magic is considered to be the magnum opus of a magician, because of having to train their imagination to picture the phenomena they want to conjure up, i.e. the more imaginative the magician is, the better their chances at making a new magic. This means they are also scientists, because they require knowledge to be able to reliably imagine what the phenomena they want. It is also dependent on the INT of the magician. The main character can create new magics reliably because of their absurdly high INT stat, modern knowledge, access to the Library of Alchias, and Instant Learning skill.

In this world all of the Middle Ages of Earth occurs at the same time, but at different parts. The country where the main character is in is akin to 10th century HRE. The continent he is in is akin to 10th century Europe. There is a country that is akin to Middle Ages Egypt. The goal really is intergalactic, i.e. they have explored every planet and star system in the galaxy, have established diplomacy with ones with civilizations, and they can interact with, and go to neighboring galaxies within its local group. No need for conquering the entire home galaxy.

I want a realistic rough estimation please!

EDIT2

The main character also teaches the principle behind the tools they make, and how to create them from the ground up.

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  • $\begingroup$ Welcome to Worldbuilding.SE! Your question does not really give enough information to be answered. How does your magic work? How powerful is it? What does it mean it consumes mana? Do you want a minimum requirement or a rough estimation of how long they would realistically need? There is too much unclear in the information you provided. It would be nice if you could improve your question to help answerers give good answers. $\endgroup$ Commented Sep 13, 2018 at 12:51
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    $\begingroup$ In addition to ArtificialSoul's questions, what do you mean by "spacefaring intergalactic country"? Does this country need to have explored another galaxy, traded with an entity in another galaxy, or conquered another galaxy in order to qualify? Given that FTL is a pre-requisite for any timeframe of less than millions of years, what FTL travel is possible and how far in Earth's future does it become available? $\endgroup$ Commented Sep 13, 2018 at 12:57
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    $\begingroup$ 1. of 2: You should narrow down what you mean with "medieval". The period of the (european) Medieval spanned nearly 900 years! Furthermore, is <our medieval comparable to the european medieval, or an asian, arabic,...? In regards to your magic, how exactly do you from these magical "functions"? Is there a magical language or some sort of special ritual to perform such a function? And, as @KerrAvon2055 already mentioned, "Intergalactic" is a really huge goal! Intergalactic = between galaxies! Maybe you should narrow down to Interstellar ;D $\endgroup$
    – DarthDonut
    Commented Sep 13, 2018 at 13:00
  • $\begingroup$ 2. of 2: How does your Mana system work? Does Mana replenish over time, or with the consumption of certain food? What happens if a magician needs more mana for magic than he has? How is the standing of magicians in society? If they are outcasts, they won't be changing much. With "main character can freely make magic", do you mean he has no mana cost? $\endgroup$
    – DarthDonut
    Commented Sep 13, 2018 at 13:04
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    $\begingroup$ This sounds like your average isekai anime so make it take 13 episodes ;) $\endgroup$
    – 0xFF
    Commented Sep 14, 2018 at 15:16

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I doubt this question is truly answerable.

If Magic makes the daily struggles so easy that instead of taking a long time constructing buildings you just execute build-my-house.exe people would have a lot more time on their hands.

Time they could either use to advance technology or magic, or do nothing that advances anything.

The main driving force of innovation is necessity and simplification

Throughout the ages mankind developed things that helped them in their daily struggles. Better weaponry for hunting (or war), better tools for construction, better housing, etc..
All those are things that improved everyday life (often with minor disadvantages - like lead poisoning from lead pipe plumbing). If your magic is powerful you would not need a lot of technology.

The determining factor is the interest of people in research

If we were to assume that people have extremely easy lives and could spend their freetime without ever worrying about nature or resources, then they could technically advance very fast. Just think about it. Every single person could do research, and even be assisted by magic! It is an unlikely scenario, but technically possible.

So we got from medival times to basic spacefaring in roughly 600 years. And we didn't have fancy magic of any kind. So depending on how powerful your magic is it could maybe be possible in 100 years.
But is that likely? Humans will most likely not invest everything into research. A lot of time and resources (and magic) will be used for wars, humans favorite sport as history has taught us. And war will be a main driving force of invention. If you are better at killing your enemies due to inventions, you will conquer instead of be conquered. Very simple concept, right?

The moment somebody comes up with intercontinental missiles to fight enemies far away we are relatively close to spacefaring already.

Can there be a realistic estimation of when they actually start building their first spaceships?

No. How could there? A lot of main inventions were dependend on a few influential or genius people. A powerful leader investing in the right scientists can achieve a lot. That is how Fraunhofer came from being a poor almost-slave to being an extremely accomplished scientist that has made huge discoveries and basically laid the foundation for astrophysics. If he had not been picked up by Maximillian I Joseph of Bavaria, those discoveries would not have been made. At least not at that point in time. Maybe a few years later, maybe several decades and possibly centuries.

The speed at which science progresses in specific areas is unpredictable

Adding magic into the world is not making an estimation easier.

And unless the time period, the magic and the world are more precisely defined, I don't see how anyone could even attempt to make a rough estimation of the time needed.

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  • $\begingroup$ You undercut yourself when you say there isn't enough information to answer the question, then proceed to provide an answer to the question. $\endgroup$
    – Frostfyre
    Commented Sep 13, 2018 at 13:10
  • $\begingroup$ @Frostfyre The criticism i raised is mostly irrelevant to my answer. My comment focuses on flaws in the structure of the question. My answer is mostly referring to a basic flaw in the premise of the question and does not hinge upon the lacking information that would be needed to answer it was answerable. However, whether it is answerable is kind of a matter of opinion. I might be wrong and the community consensus really likes someone elses approach to estimating the time needed. Such an estimation would be ridiculous if it would not need the information i asked OP to provide. Don't you agree? $\endgroup$ Commented Sep 13, 2018 at 13:17
  • $\begingroup$ I never said the answer was bad; in fact I agree with it. Was simply pointing out the conflict between comment and answer existence. $\endgroup$
    – Frostfyre
    Commented Sep 13, 2018 at 13:42
  • $\begingroup$ @Frostfyre Yeah, i get what you mean. But i think the reasons i gave for it being unanswereable in the comments and in my answer are two very distinctly different things. I added a sentence to the end of my answer stating that without any more precise definitions by OP i do not see how anyone could even attempt to reason an estimation. $\endgroup$ Commented Sep 13, 2018 at 13:44
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In our part of the universe, galaxies are millions of light-years apart.

Without faster-than-light travel, it will take millions of years to establish an intergalactic society.

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Billions of years

This question is answerable with an estimate now because the OP states:

"The goal really is intergalactic, i.e. they have explored every planet and star system in the galaxy"

First, let me (again) quote Douglas Adams: "Space is big. Really big."

The Milky Way has 100-400 billion stars and at least 100 billion planets at current estimates. The requirement is that one country explores all of them. Just for reference, not all of Earth has been thoroughly explored yet - only relatively tiny sections of the ocean floor have been explored in detail, many cave systems remain unmapped and we are still discovering new species all of the time.

Assumption time:

  • FTL works at "Star Wars" speeds, where trips in hyperspace between stars typically take minutes to hours. (There is an inherent contradiction between the statements that "making an X-fighter type spacecraft with FTL capabilities is relatively easy" and "Magic can be used to break the laws of physics, but the mana cost becomes impossible to overcome" that I am deliberately ignoring.) Once we know that interstellar trips are taking hours at most, the rest does not really matter.
  • The maximum "country" size on an Earth-like world is about 2 billion people (ie about 150% of China's current population. Note that as soon as you start having colonies and other countries doing exploration for you, your country is no longer meeting the stated requirements.
  • "Exploring" a typical star (including smaller than planet-sized satellites) or planet (including satellites) will take 100,000 people with Star Wars level technology about 100 years once they get good at it. That may sound like a long time for a lot of people, but not once you start trying to assign people to tasks. The time would be shorter with a lifeless system, but potentially much longer in a system with life in it. Remember that Jupiter is "a planet" - so exploring it requires covering all of its moons as well.
  • There are 500 billion targets for exploration in this galaxy - whether that is 100 billion stars and 400 billion planets or the other way around. Freely admit this is a wild guess, because we just do not know yet.

  • About 1% of the country's population will be actively engaged in exploration. Once the logistics "tail" is added in, it is actually a huge economic commitment to have that many people actively deployed at once on a permanent basis.

Crunching the numbers - there are 20,000,000 people conducting exploration on 200 separate targets at any one time. After 250,000,000,000 years you will be finished - except for your country not existing any more because the Sun only has another 5,000,000,000 years before it becomes noticeably less friendly to life on Earth. Most of the exploration targets will be suffering in similar timeframes.

Even if you posit a mere 1 year per target, 2.5 billion years makes all other stages in the development of your country irrelevant.

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  • $\begingroup$ As far as I know there are 2 theoretically possible FTL travel methods: the Alcubierre metric and wormholes (not the Einstein-Rosen bridge kind). I am not considering those as breaking physics :D What I meant by “Magic can be used to break the laws of physics, but the mana cost becomes impossible to overcome” with regards to FTL is accelerating to the speed of light and then overcoming it. “The X-fighter type planes with FTL capabilities” use the Alcubierre metric for its FTL travel method. $\endgroup$
    – Aphrontos
    Commented Sep 17, 2018 at 7:09

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