who will makes differences?

#1
let's say i've a typical sword-&-magic medieval world, i'll then throw in that world, a person
in which scenario down below, do u think that person will make the biggest impact to that world (positively)? if u've ur own theory/scenario, spill it too :D
1. a physicist
2. a chemist
3. an engineer
4. a programmer
5. a mathematician
6. a businessman
7. a politican 
8. not a professional/expert but a 'jack-of-all-trade' with little bit of everything instead
etc.

so, let's start :)
*my opinion is that an engineer or a programmer maybe able to contribute a little bit to the world's advancement
1. with the other world is a medieval world, an engineer, eventhough may not be able to bring up top-notch modern technologies, would still be able to "invent" things like better weaving machines, toilets, steam engines, weaponry, siege engine
2. if ultilitizing Earth's medieval, reconnaissance or colonial era engineering knowledge, maybe he/she will be able to make Earth-inspired magical machines
3. maybe there will be golem, a programmer maybe able to ultilitized his programming knowledge for golem crafting 


*suprisingly (well, maybe not, but still), a physicist, or a chemist, may not make a big impact in another world, or make any at all
1. it's another world, physical laws may be different in that world, as such, all the knowledge can only be ultilitized as "advises" at most, further corrections 're needed
2. considering Earth's history, it takes thousands of years for science to really sped up on Earth, a sword-&-magic medieval will probably have it much worse with religions, wars, magics, etc. 
3. even with a large amount of advanced knowlegde, the lack of equipments will make it hard to find evidences for theories, etc.

*a mathematician maybe of used with mathematic being likely unchanged across worlds, though those pieces of knowledge could be covered by dust because of the lack of usage
1. being in a world with no physics, chemistry, etc., math actually may very well backwatered and stopped at the level of addition, subtraction, multiplication, division, which makes it possible for the mathematician to contribute something new
2. on the other hand, derivation, integral, or any other 'advanced stuff' only get 'discovered' because there're needs for them in other fields such as physics, chemistry, etc., meaning the math knowledge has very good reason to sleep soundly under blankets of dust

RE: who will makes differences?

#2
That's a real hard question, mostly because 'a medieval world with swords and magic' is just too generic. Like in "A Hero's War' Cato is an engineer and he's super useful because, while magic exists it hasn't really produced anything superior to modern tech - the magic in that story is sort of stunted and under-utilized by the natives. So Cato can really show off his knowledge as an engineer to great effect. But then in "Knights and Magic" the MC is a programmer and *coincidentally* piloting a big magic mech suit is a lot like programming. In short your character can be anything and then you just write the world to accommodate that specialty, because with magic you can just wave your hand and say 'a wizard did it'.

That said if you take the magic out and your just 'improving a medieval world' I'd probably bank on an engineer - since a lot of their knowledge can be practically applied. They'd know a lot of practical mathematics and probably chemistry too. But I'm mostly blowing smoke because I don't really know the different impact a phd level chemist or physicist could have on a world like that. And it's still really ultimately author's discretion, you could write that he was a super good cook and then just have him only stumbling into situations where a cook was desperately needed (the kings banquet is tomorrow and the head cook ran away! or something).
~writing is hard~

RE: who will makes differences?

#3
i think, let's just go with the common setting of world that people use, a world with mana that can change reality but otherwise, still operate under physical laws, maybe with some small tweaks here and there, such as instead of Gravity = G*M/r^2, with G = ~6.67*10^-11*m^3*kg^-1*s^-2, it's some G' = 7*(....), or instead of c = ~3*10^5 km/s, it becomes 3*10^4 km/s

it seems engineers probably make most practical, observeable, material impact in short time eh. A mathematician will probably make a 'subtler' long-term impact, while the one having it worst likely to be physicists, more so if he/she is aerophysicist or astronomer
people brewing things all the time, so i think a chemist should be able to make use of chemistry somewhat, could very well make 'bigger changes' than a mathematician
there's still possibilities where a chemist will be 'burned on stake' for 'practicing witchcraft' and a physicist for 'blashphemy/heretic' though
what about a politician or a businessman, well, maybe not a businessman, but probably, a economist, or finance analysist, etc., then?
a politician, while being in a world filled with king, emperor, or other forms of hierachy may not 'play' politician as efficient or effective like when he/she's in modern Earth, but i don't think he/she would be totally useless or barely survived
i certainly not know shit when it come to politics stuff so it's up to some professional wandering the site then :p
maybe while an engineer's making practical, immediate changes with pieces of technologies, or a mathematician's providing chances for changes by giving out math knowledge beforehand, a politician or an economist may speed changes (which may already under going or may start in the future) up a little bit, so things come earlier, faster than they suppose to be, assuming that they're given the chance to practice their fields
for example, bringing all the knowledge of economy, finance, politics of modern Earth back into 12th-15th cent. medieval era, certainly things won't change at first, or it seems to not change at all, but with those knowledge known, we may have some nice stuff to see in 16th cent. that we should only be able to if we leave the world to develop naturally

RE: who will makes differences?

#4
The problem is that without some prerequisite technologies, you can't advance science much.
For example to introduce steam engines, you need a decent metal industry in place, and that take at least a few generations to set up.

I think that the people that can make the most of itt are people that know how to manipulate the human nature, and know some impressive but simple tricks.

Imagine a froud, that make gunpowder to make a small explosion and claim to be the hand of God. He is either killed outright or made into a Guru.

Therefore, more than expertise, I would rate based on people manipulation skills.
First would be Politician, businnessman and Jack of all trades
Then would be craft that deal with law of physics. Chemist, physicist and matematician
Finally, the least impact is from people that needs an industry to shine. Engineer and programmer.

Just my opinion.
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RE: who will makes differences?

#5
It is an interesting question. The problem is that the result depends a lot on how exactly we measure it. Some of the changes that can be accomplished through the knowledge and experience these fields bring have a lot of requirements, and may take more time to come into effect than others. I will therefore describe 2 lists, and then give comments on top of it.

The first list is for the expected impact. Expected being the mathematical term here, which in laymans terms would be average or mean (the mathematician will know that expected is a probabilistic term, while average is a statistic term).

1) Engineer - They tend to have the knowledge of how to actually build modern technological items, and can at least "invent" a lot of stuff easily.
2) Chemist - Like engineers in practical mordern knowledge, but with a different limit to the scope (only chemestry, and many of the things that use advances in chemestry requires other inventions they cannot do themselves).
3) Buisnessman - There are very little new knowledge that can be exploited, but they are very likely to be able to get the resources necessary to make larger changes.
4) Physicist - While there are a lot of things they could change, it is quite hard, but the rest either have similar odds, or just dont contribute on a enough large scale.
5) Jack of all Trades - They dont tend to have enough knowledge in a field to really advance it significantly, But they are very likely to be able to apply these changes.
6) Politician - They could potentially advance the social structure, though most modern people have the same potential, they just have a larger chance at succeding at it. Their problem comes from both getting into position to do such, and from socierty probably not being in a position ready for much change anyway.
7) Mathematician - Most of their knowledge is fairly abstract, and while it will help, the conditions are though and the advances in math would probably come around by the time most of it was needed by other fields anyway.
8) Programmers - Unless magic has some aspect that requires programming, you are just left with a poorer mathematician that relies even more on tools not accessable in the new situation.

With that list out of the way, we can move on to who has the highest impact potential, meaning that how much they could impact the world if given the prerequsit resources and time. Note that "Jack of all trades" 's position depends entirely of how deep their knowledge is in the spread out fields. I will assume they only have superficial knowledge in those fields in the ranking here, but if they had the right fields and was good enough at them, they could potentially go all the way to the top.

1) Physicists - Given time and resources they can produce enginers, chemists, mathematicians, and programmers of only slightly lower quality than typical of modern day, they also have the necessary attibudes to deal with other new fields of study and advance them significantly. The main limit here is lifespan, so if magic can be made into increasing it then the impact can become huge. They are also proffesion with the most advantage in learning magic. The most effective variant would problably be a condensed matter physicist.
2) Mathematician - They are the second most likely to master magic, and advance that field. This is especially relevant if magic requires a lot of complicated formulars. The reason they are behind physicists in terms of magic is that physicists tends almost as much math as a mathematician (they have advantage is strictness and obsurity), when considering that mathematicians also have to specialice in some field, and their gain in that area is not enough to offset the intimate knowledge and intuition about how the world works, that physicists have. Phycisists are also more suited to study new fields than mathematicians (there are several fields in reality, which are basicially "this field as seen by a phycisist", and physicists are often employed not in their capacity as physicist, but because how good they are at modeling all kinds of new problems). They could also establish schools, but their product is significantly less than phycists. If we discount magic, they would be much lower on the list.
3) Chemist - They also have a good chance of mastering magic, especially alchemy related magic. and they also know sufficient math that they can do well in math heavy magic versions. They can make schools producing chemists and lower grade mathematicians, which means they are very close to mathematicians above, and are mainly below because math heavy magic is a common form of magic, so the advantage pure mathematicians have there are larger.
4) Engineer - They are still very likely to do inovate and create a lot of new nice things, and also do very well in magic. They just dont do as well in magic as phycisists, and chemists and mathematicians would have a larger advantage if they type of magic is used, though engeneers are more likely to be good artificers. They mainly loose out in the power of school building compared to the above, since scientist level can generally produce engineers over time, but not really the reverse.
5) Programmers - They are pretty much inferior to all of the above for the simple reason: all of the above professions tends to know how to write programs to some level. This means that they only get an advantage in their advanced types of programs compared to the above, which is the least likely area to be important in magic. To top it off, their school power is soo much lower, they could only produce inferior mathematicans, all the above could produce better mathematicians. To gain any real power here, we need some of the higher levels of programmers, not just an average programmer. They are above all those below because they would still have an advantage in advancing magic, which one of the below have, especially if it is their type of magic.
6) Buisnessman - Hallo mister trade mongul, the world moves with money.
7) Politician - There are a lot of nice things to do, but all of the above could innovate socierty in the same way, politicians is just more likely to work better as rulers in practice.
8) Jack of all Trades - There is no real advantage to truely leverage given all those extra resoures, at least not to a significant degree compared to what the others can. They are lower than politicans because, well even they have an advantage in creating a better socierty, these dont really have that.

These arent really set in stone, especially the Jack of all Trades, for both, as it is hard to really evaluate them. There is also a lot of dependency of what subfield people have specialiced in. A microbiology engeneer would probably have a lot less of an impact than one dealing with more traditional crafts, as those types would be able to make their own tools, and improve on those tools until close to modern standards have been reached. Magic is also an important element in the above, if we disallow magic power or just make it much less significant, we get a different list, assuming they still get the same resources as the last one:

1) Physicist - The power of their schools still roam suppreme in changing the world over time.
2) Engineer - For the same reasons as before, their schools power are only slighly worse than chemists (but much worse than physicists, as they could produce these engeneers), but their broadness of fields makes them come out slightly ahead, and they would still make more innovations.
3) Chemists - For the same reason as before. Their schools would produce chemists, mathematicians, and some subtypes of engineers, but they would still lack some important fields to improve their tools to make all the mordern necessities, it is close though.
4) Businessman - They can mordernise the economics to a large degree, and build huge cooperations that will dominate the world.
5) Mathematician - They can by schooling build up businessmen, but of lower quality, as it would mostly be derived, and they would lack experiance of real world economy to do much with it. Their schools are not all that powerfull either.
6) Politician - For the same reasons as before.
7) Programmer - They dont tend to know the fields of math necessary to do business (specifically analysis), though some computer scientists with the right specialisation might do. They are therefor left with just the power of inferior mathematic schools, which is even worse than the advantage of ploiticians.
8) Jack of all Trades - For the same reasons as before.

So, how did I come to these conclusions. Well, I have university degrees in both as a physicist and computer scientist, so I know the cabablities of those, and I was close enough to mathematicians and chemists to have a good expextation of what they can do. For engineers I use the following rough rule. Scientists and engineers have a similar relationship as the one between engineers and craftsmen. The first produces the information that is the base of how the second go about things. For instance physicists produces the knowledge, which most engineers use, as their version are commonly considered as "rules of thumb" by physicists (meaning they arent the true laws of nature, but usually good enough in practice), while engineers will figure out how to best build things, which are then used by craftsmen as "best practice" or just how things should end up as. Another way to put it is that the form have theoretical knowledge and the latter have practical knowledge. This is why engineers are so high up, there are already craftsmen in the world, so if they apply their mordern theoretical knowledge they can easily get new innovations made. Physicists are fairly removed from a lot of practical knowledge, so they would have to get funding to first reseach pratical problems, like how strong is this metal alloy, or how to make this tool, but if given time they posses the knowledge that form the rules of how an engineer should do things, so they can get them as a result of building a schooling system (an academy for privileged is still suficient, it doesnt need to be schooling for everyone). Chemestry have a lot more direct practical knowledge compare to physics, so they are a lot more likely to do well, and they also have an idea of how to produce many of the resources they need.
Business is mainly a speculation, based on having someone come by and talk about economy in some math course, and the result was: It seemd like they were trying to reinvent "simple" math with new names, so someone with good math skills in the area of analysis (mathematicians, physicists and chemists), should be able to reproduce many of the their theorems, but mostly would just not look too much in that direction.
Politicians often have inferior education to most academics, at least in the type that can change the world, so they dont bring much knowledge that can change the world radically, and medival times were not at all known for letting skill in governing decide whether you could become a leader, only whether you would lose leadership that you already had. You needed to either be a noble, or at least have some connections and/or resources to become some kind of official.
Jack of all trades, are really hard to determine, so I mostly just assumed a common extra knowledge, such as decent cooking, hourse repair and such, all of which would not really be able to bring any huge changes. There would be a few modern nicities, like toilets and such, but nothing too game-changing.

RE: who will makes differences?

#6
:whistle: that's a long analysis :v
though u maybe little bit "over evaluate/estimate" a magic-&-sword medieval world's abilities n' capablities
considering it's based off medieval Earth with magic as a minus(or plus), technologies, knowlegde and the like in that world maybe "more backwatered" than medieval Earth
which means, it may not require a highly skilled, professional person to change things, a highschool student may actually capable of making changes with his even though limited, but still overwhelmingly advanced knowledge in chemistry, mathematic, etc.

eventhough Gunpowder, Toilet, Water pump, relativity, gravity law, Newton's 3 laws, "Earth's a sphere", derivation, intergral, etc. may seems so basic to a modern person with good-enough education, every single one of them is already "ahead of time" enough by itself

which makes a "Jack" sometimes can be more influential than a professional, considering he eventhough might have only as much as 1/10 of what others know in 1 certain field, the knowledge in each field 're still significant enough
furthermore, a mathematic maybe able to create a "high-ground" n' "steady foundation" for mathematics, and a little bit of physics, or chemistry or programming, a "Jack" can create foundations for all kinds of field, and have them advanced by "real professional" or talented people in that other world of those fields
(and although i used those inventions as example, a person might know much "higher" stuff than just them)

and if u think the knowledge of those things mentioned above rather basic and people of other fields know it too, well, u maybe suprised it's not so
for example, there 're still people around this modern world ACTUALLY BELIEVE (not trolling around YouTube) that Earth's flat, 80% US Adults 're 'scientific illiterate', 1/4 of the asked answered incorrectly the simple questions of "how long it take for Earth to cycle around Earth?" n' "Is It Day or Night that's longer in Winter/Summer?"
- the statistic taken from 'Space Chronicles'
- let's just suppose those numbers 're true, then let's multiply it up to the World scale, there will be places that have it much worse, places slightly better, etc. but overall, there're things that u may feel normal that 're suprisingly "advanced" to even Modern Earth people

Lastly, suppose Golem 're real in other world, then u may need to consider that EITHER Programming may actually be much more convenient n' easier in that world OR Programming actually very advanced in that world, which, makes a programmer EITHER suprisingly capable OR utter useless
-----------------------
anyway, moving on, we've been sticking with the 8 scenarios, what about something different? a educator, a doctor, a biologist, a ecologist, etc.?
or let's move entirely away from "science n' technology", what about a feminist, a pope (any religious organization's leader(Catholic, Othordox, Buddism, Islam, etc.) (person of a ideology/religion, in short)?

though i highly doubt people maybe able to influencing others of an entirely different world into their beliefs if take into account the fact that Medieval world ('n a society with magic at that) tends to be superstitions and all :v

RE: who will makes differences?

#7
None of the above.

The first four professions rely extensively on the modern equipment and faculties, and are basically useless without them. A mathematician is probably best suited to have a lasting impact, but they will probably have no one to relate their knowledge to - everyone in the era is way too behind to find modern mathematics useful or applicable. A businessman would be *completely* lost in the medieval economy (it was fudnamentally different from the modern one), and a politician would be in absolutely no position to use their talents (positions of political influence are largely hereditary and completely out of reach for an outsider). A jack of all trades would combine all of the problems above with even less applicable knowledge.
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RE: who will makes differences?

#8
A jack of all trades is one settings most likely to do decently well in another world, and there are some common knowledge things that can be used, especially related to hygene (toilets/running watera/and so on). The problem is that most of the things we know are not directly applicable, were known by a minority (decent math+writing), or simly requires resources not readily or at all available. For example, knowing newtons laws doesnt really do much by themselves, and you need to be trained in a related field to be flexiable enough in your application of them to really use them for all that much. On the other hand, most of the tools and materials we use to make things today are just not available in the middle ages (aluminium/alloys/rubber/plastic, most chemicals) or just very restricted (good glass/mirrors, and steel).
This means even though we know about a lot of things, we cannot use very much of it to make things in those settings. The problem with a jack of all trades, is that the other people would know most of the same things, and unless his/her skillset happen to include how to make the specific things needed from the ground up, then he/she only have a very slight edge compared to the others, so it is hard to make more impact on the world than the others.
Remember, when we have a list of who is most something, and we add a flat amount to each of them, then the order does not change. Think: if we were counting which fiction has the most view, then the order would not change if you added one person veiwing them all, because they all had 1 more view, so there was no way for one of them to get ahead by this.

I am not sure if the "overstimation a magic-&-sword medieval world's abilities n' capablities", is based on the last 2 listings. Those ones are basicly about the potential for impact over a long time, so if someone with ample time on their hands can derive how to deal with those problems, then it will be counted as solved. The first one should be better balanced for this, and I mainly assumed that one could get a blacksmith and/or a glasblowing to do a lot of the rough work, as there were plenty of people skilled in those proffesions (at least the first one) in mediaval times - though they dont have the advaned knowledge to make really good things.

Concerning programmers, it is really a pitifull thing, mostly because the amount of knowledge in programming it takes to be called a proffesional programmer, at least when compared to some of the other options in the list. At least physicists and mathematicans could easily have taken courses during their standard education that would be enough for them to go out and take a job as a professional programmer. That doesnt mean you dont have people that have vastly more knowledge about programming than just reaching that low treshold, but those are often refered to by slightly different names (such as computer scientists, software engineers and so on). Basically, your average programmer doesnt really have much that the other proffesions mentioned above doesnt have (physicists, mathematicians, probably engineers and chemists too), so they dont really get that much of an advantage. Worse still, most of those are specialiced in some specific language or solution type, which is definitely not the form needed for golems, and to top it off they would typically not have the general knowledge and skills necessary to translate them to different forms. Think of it like this, if you have a Java programmer, is the golem going to have Java installed by default, if it does, then that indicates that the amount of knowledge in terms of programming is already ahead of this specific person, and if not, then he/she doesnt know how to make it run on Java, because he/she doesnt know how to setup a operating system and compiler.
Most programmers doesnt have sufficiently broard skillset bootstrab a golem/robot or a computer. You need something like a "full stack developer", which are not your average grunt programmers.
If you have these kinds of programmers, then yes you could start to see some impact.

Concerning whether physicists, chemists, engineers, and programmers depends heavily on modern equipment, then that is partialy true. Programmers are the ones depending the most on it, followed by physicists and then chemists and engineers. Without special magic, programmers cant really do much without computers or equivalent. Physicists rarely know how specifically to build things, but they could figure it out with a lot of work by deriving it from basic principles, and especially the experimental variety would not be completly lost. For chemists some of their tools will not be there, but plenty of them should be replicatable if you give a hired craftsman specific instructions, that they typically have a decent grasp on. Engineers would not have their calculators and modern materials, but they have the specific knowledge of how to get craftsmen to make exactly what they need, so I would not expect them to be all that lost.


Mathematics is easily overevaluated in my oppinion. Yes, mathematics is important, and a prerequisit for much information, but that is also its problem. See, if someone have the knowledge of a certain field, they would also have the mathematical prerequisit knowledge, so a mathematician is mainly left with all the mathematical knowledge that was not realy a prerequisit for any of the things that needed to be used for the immidiate advanced. Furthermore, it suffers from the problem that mathematics by itself is not really all that powerfull a tool. Yes it helps certain things, but to really make use of it, you need to develup the things that makes use of it first. That is where the catch is, because by the time the thing needing the math would have been develuped, chances are that the math would naturally have developed to a sufficient stage anyway, so injection of additional math didnt really get to change much in the terms of evolution of the sciences, only give a slight increase since someone might fall over things slightly earlier and have the math to deal with it.
In other words, math is important, and necessary for other things, but boosting it far ahead doesnt change much, because it doesnt make the other fields got ahead by itself.

RE: who will makes differences?

#9
what i meant about "overestimate" is that, u seems to associate physics, chemistry, etc. too much with "modern", and leave out the fact that before all the modern thingies, there's also the long ages before that where knowledge is more scarced, les advanced, meaning even the not-so-advanced knowledge we know today is actually suprisingly advanced
u though, also a bit "underestimate" how much impact a little bit of 'advanced' knowledge could do, it's quite obvious actually, just rollback time a little bit to the time after each of all those old inventions on Earth get discovered (explosion, radio, calculus, gun, steam engine, airplane, etc.)

u assume that all the requirements 're modern stuff too much
physicists don't only going searching for stars, or tinkering with atoms with modern tech. u know
physicists, engineers, etc. pre-modern age certainly didn't need all those high and mighty electrical equipments for their jobs before machines became a thing

and the problem is that the person certainly doesn't 'work' alone, what's the point of putting them there, and giving them no environment to get things started, because if it's the case, then it really doesn't matter what kind of person u throw into that world, they all would become useless because there's nothing they can do or get started with

-the engineer certainly have to given a workshop, materials and (available-in-that-world) tools, assistance, etc. to work with (anything as long as not Earth-origined)
-a physicist may be assisted with engineers, the guy may not be able to build a machine himself (a steam engine for example), but he should be able to draw a rough blueprint of sort, and have the real-deal-engineers/craftmen to make it happen
-a politician may be given a post in goverment
etc.
for the scenario to make sense (though there're scenarios that just not works)


let's have examples, steam engine, gunpowder, the 2 things that often come into people minds the most when it come to this type of situation
-suppose gunpowder overpowers magic, certainly, people at ancient up to before industrial era didn't have the nowadays-big-ass-factories to mass producing ammunition, yeah? so, that's certainly 1 thing u can create without modern machine (eventhough not as efficient when u have factories and the like)
anyway, with gunpowder being a thing, weaponry picked up, wars picked up, magic become useless, not utterly, but still lose its influence
->and that, is "impact"
before: people throwing spells at each other, lining up with spear, sword, crossbow, riding horse into battlefield and the like
after: guns, guns all over the place

-steam engine, meaning better transportation, logistic, mining, productivity, trading, etc., machine become a thing, wars kick off because of the need for resources for production, slavery increase for larbor, better equipments, technologies to increase production efficience+effectiveness, factory become a thing, then comes bigger classism, capitalism and communism and whatnot, then revolutions, fall of feudalism, blah blah blah, like what happened on Earth
->that, is also "impact"
before: horses, carriages, etc., stuff u may commonly see in medieval magic-&-sword world
after: trains, factories, machines, maybe republics everywhere, perhaps a certain United State of Something Something after a few decades, etc.


it may seems exaggerated, but that's actually the rough outline of a chain of stuff that could happen
certainly, it may not all happen in 1 lifetime, but nothing happens in 1 lifetime
and impacts only start to come up visibly after years, decades after things get started
it's also not only about the imediate impact that they create, but also the side effects, the aftermath ,etc. like a nuke, or reaction in a nuclear plant

it's not about a guy come into new world with knowledge and the world get impacted instantly in shortly after a year or 2, but it's more about, like, 'what'd the world look like after 10 years, 50 years, 100 years, 200 years, even after he/she die?'

u may say that even if the knowledge is provided, thing may not speed up at all, well, it maybe true, given it's similar enough to Earth, that's why people only discover certain things at certain point of time, or certain events happen at certain milestone of history

however, this is fantasy world, things get different and certainly much more convenient with magic's presence

the point about math is useless by itself because there's nohing to practice on or apply on, is correct, that's why derivative, integral, etc. got invented at the time they got invented
but in this case, it's slightly different, because it's not math being 'invented' alone, and similarly, a physics/chemistry knowledge get 'discovered' alone
on Earth, math knowledge is discovered due to the need of it in different areas, it's the result of demands
now though, it's discovered in pairs, with not only the knowledge itself only but also its application, for example, u introduce calculus, but certainly u don't introduce it alone, but also explain how to apply it in other fields, aside from the already-known-on-Earth applications, there maybe stuff like calculating spell's efficiency, effectiveness, golem's mana consumption, rate of change in mana consumption, statistics, blah blah blah
say if u have a 'tree o' tech.' of {1-2-3-...-n} and 'tree o' knowledge' of {1-2-3-...-n} coresponding
if K(n) being introduced before T(n-1) being finished invented yet, meaning it's temporarily useless, however it'd still accelerate the discovery and invention of T(n) when the time come, furthermore, if u introduce K(1) early, it'd also mean T(1) deing invented early, leading to all the other inventions after that being invented earlier, the gaps that u see in Earth's T. also pretty much non existed because neccessary K. is available

RE: who will makes differences?

#10
With all the wall of text answers I see here, I decided that I'd rather just give a very simple one.

Mechanical engineer + Chemist or just a dual course mechanical and chemical engineer.

Steel mills/ pouring steel by the tons + Haber process/ making synthetic fertilizers from air = Industrial revolution

OF course, caveat is that this person may spend the rest of his life trying his best to first try and check off the prerequisite techs and has infinite money and political power behind him. The right man in the right place can make all the difference.
They said the world is ending.
They are wrong. Its only changing.
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RE: who will makes differences?

#12
Math knowledge would speed up the discovery of other things, yes. I just postulate that that the speedup would be minor. Normally math is already ahead (in terms of when something is needed) of other fields, so if you are 50 years ahead or 500 years ahead the difference would not be all that great, as most of the things needed would be there by the time other parts of science gets to them. Some of the standard forms of theories we know today were originally described with different math, and later converted to more convinient forms of math, when such things were discovered. Another problem here is that math knowledge too far ahead will easily become so obsure for the common user, that after some generations the people that would need it for some discovery would not be aware of it, especially since it might not have a use yet.


One of the things I have seen several authors do, is someone going into such a situation and building all kinds of things, that they realisticly have no idea of how should be built. A lot of invensions and their current form relies heavily on some details that most people arent aware of, and if you dont know them then your try on replicating it would make your attempt at a car look bore like a childs toy bob-card (or whatever those ones are called in english).
Let me take a few examples that you mentioned:
1) Guns. Guns were introduced in the late part of the medieval era in the west, and were know for far longer in the china. While those things were used back then, they just werent all that good.
Before we can even get started on the parts of the gun, must people might not even know how to produce black gunpowder. Yes the charcoal+sulfur+saltpeter is commonly known, how to actually get sulfur and and saltpeter is not or just recognise them. The processing is not entirely risk free either if you dont know what you are doing.
The first gun problem is that the actual increase in power compared to crossbows first comes when one can produce barrels/cannons of sufficient level of quality. Without that the gunpowder cannot be used to all that great effect, or just explode in your face. There are other things you could try to make, but much of the firepower we have nowadays comes from more sophisticated forms of explosives.
Next is the design of the ignition. It turns out that the one we use in modern times (1900+) uses several different types of explosives, none of which are black gunpowder, and you cannot just use the same ignition form without it.
What about precision, it took a long time until guns became even remotely close to precise, there is a reason that they used massed lines of people fire guns at each other in a long periode of time, while it was still quite feasable to do a charge. It was only when precision and fire rate was increased sufficiently that they became such overwhelming weapons.
For fire rate you need to design at least a back loaded gun, or preferably some kind of semi-automatic system. It comes with a lot of design problems, on how to have propor seals, ensure that everthing does not just fall appart, and there are a lot of moving parts that need to be designed to work well.

2) Steam engines. I am not sure you are aware of just how inefficient the original steam engines were, and how many small mechanical invetions were needed to make use of the steam power in the form you want. There were a lot of problems with steam engines originally, and it was only after it had be innovated upon several times that it really took off. Remember that you could use both wind and water (streams/rives) to power mechanical contraptions beforehand, so it needs to reach a certain level before it becomes usefull.
There are also all the details of how to get a steam engine to actually work, there are several small details that most people are not entirely aware of. Such as good designs for the air vents, and how to ensure that the air enters and leaves at the right time, and not also at other times. How to ensure that the steam engine runs smoothly, and also not explode on you.

3) Light bolbs. We commonly hear that Thomas Edison invented the light bolb, but if I recall correctly what he did was have a team of people help him find out some of the important material details of what makes an effective light bolb, as there were already electric light bolbs beforehand, they just werent very good. Specifically it was the kind of thread used (possibly also the air part, but I would have to check up on that). This might not be a common thing people would invent, because you would need electricity first, but it is one example of easy misconceptions.

4) Steel. Many people consider knowing about steel common knowledge, but there are 2 great problems. First most of the processes require iron to be melted, so you need to know a method to heat it up sufficiently. Magic might help you there, but most of the medival world did not know how to reach the required temperatures, and unless you also know that you cant really do much with it.
Second, one of the common methods is to "blow air" through the melted iron, but for this you need a specially designed container (I dont recall the correct term for it), with holes in the bottom, and you need to prevent the molten iron from just going through those holes, and find a way to blow the air through it. Oh and what material would it be made out of. An older method relies on building a special kind of overn, which creates the necessary conditions. If you dont know how to build that either, then you are going to have some troubles.


There are more, but it basically comes down the the following problem: The average person miss some crucial details in their knowledge, and it might take them more than their lifetime to figure out how to solve it, and they would have troubles passing their ideas to others to further invent on them (example, Achimedes wasnt exactly following by an equally famous inventor, you need more formal form of knowledge to do that, such as for the old greeks).

I should probably mention that I expected most of the changes to happen within roughly 100 years, especially for the "school potentaial" type, which might go a bit further. Concerning about whether people work alone and such, I would refere you to the difference between the first list and the others. The first list takes account for how dificult it would be to get them in position to do those things, the second and third assume they get into those positions.