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Having concepts is not necessarily the same as having written symbols. In our culture, we are able to handle different degrees of infinity without each having a distinct symbol. In the computer and database world, we are to varying degrees able to handle variants of zero/empty/unknown/null/void/...
I was surprised when I many years ago learned that there was (maybe still is) a 4-value standard code for sex, from long before the Pride age, each represented by a single digit, none of the alternatives being zero: Male, female, irrelevant and undecided. It was used e.g. by railroad transporters' reservation system: For an ordinary coach with seats, the sex was irrelevant. For a sleeper reservation not yet sold, the sex was undecided. In the old days, with three bunks per sleeper compartment, you could buy a single bunk, and the two others were marked in the database as male or female, according to your sex. Railroad companies managed to handle it, even if there were no specific symbol to represent the four sex alternatives.
I am 100% convinced that the Romans had a concept of "I owe you nothing!" or "We have reached the destination - there there is no remaining travel", even if they did not have a mathematical symbol for it. We don't have a symbol for an unspecified value, unless we introduce an indirection concept, a pointer to a value and give that pointer a void/null value. It doesn't exist in our number system; yet we are able to cope with it.
And yes, I will defend that position until you come with something convincing.
Well that's your prerogative.
We live in a free will realm, that is to say: A responsibility realm, is the same thing.
This basically means you can act, speak or think the way you decide, and stick whith the consequences, both pleasant and unpleasant; sooner, later or simultaneously, if out withdraw the factor "time" from the equation. ( equating it to NULL )
Too busy waging war to have much time for "pure" R&D. Mass "publishing" (Gutenberg) set the ball rolling. Information sharing. Today, it's called "the internet". Leveling the playing field (if you choose to use it).
It was only in wine that he laid down no limit for himself, but he did not allow himself to be confused by it.
― Confucian Analects: Rules of Confucius about his food
Every "Technology" has a predecessor technology. You can't have a toilet seat(N/A until 18th century) without a plumbing, running water and a sewage - read water pumping stations. You cant have a radio without basic understanding of electricity. You can't have electricity without advanced metallurgy. You cant have advanced metallurgy without understanding of chemistry. You can't build structures and super structures without understanding physics "Strength of materials". And pretty much list goes on.
Lots of people therefore conclude that no technology has been more advanced than the current one. That does not always hold true. One branch of technology, one society, may have developed to a quite advanced stage. Then some other society starts branching out, from a much earlier predecessor, a different kind of technology, which develops slowly while the first society is destroyed by war, epidemics or whatever. The second one may be the most advanced at the moment, but not the highest ever.
And there is the question of metrics. While we think microelectronics is the greatest thing since sliced bread, other cultures may ask: What do you want that for? What's the real purpose of this tile with colors on one side changing all the time? What is the value of that? Why do you all feel that you are completely lost without it in your pocket? We have developed along quite different lines...
You can't have a toilet seat(N/A until 18th century) without a plumbing, running water and a sewage
The Romans had a quite sophisticated system of water delivery and sewage removal in Rome. One of the duties of the Praetorae Urbani (plural?) was to ensure that the adjutages of the pipes were not too large, so that private dwellings would not take more than their fair share of water.
Note that these were gravity fed; no pumps in the modern sense existed.
You cant have advanced metallurgy without understanding of chemistry
The Romans (and the Japanese, for that matter) managed to produce very good swords by trial and error. While the Romans did not know why the ore from certain mines made good steel, they certainly knew how to use it.
Europeans (and other cultures as well, but I'm less familiar with them) were using impressive technology long before the modern Solid-State Physics was known. Just look at some of the Roman aqueducts (still standing after more than 2,000 years), the medieval cathedral churches (tall walls, glass windows, support with flying buttresses, etc.), sailing ships, and many other examples.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
I am a hobbyist historian, and if there was something very different between the Roman Empire and the 18-19th century and that would have been the rise of the middle class. There was no such paradigm during the Roman Empire and it is commerce that drives the development of technology.
It would also explain the excellent examples of technological practice during the Roman empire but in limited examples. The technology existed but was not readily available unless you could pay for it. Whereas those two elements were resolved ~1800 years later where more people had the resources to leverage tech and subsequently the remarkable change.
This is also highly evident today with the low-cost proliferation of tech, and the availability of information. Imagine COVID hat hit during the 1990's? Video conferencing was 'available', but for the rich. No one could really work from home, and that would only be possible if you could afford the cost of a PC and the 14400 dial-up modem - so inefficient and limited.
Hmm, Actually, the first couple of passes of the plague had a big effect in stirring the social structure, BUT.
The printing press: Gutenberg's about 1440 ( much slower printing before that ) by 1500 thee were presses "all over".
Paper: possibly spread to the Islamic world from China ~750, hit Europe 13th century. ( Not as "good" as parchment but much cheaper. )
Compass, probably late 12th century in Europe. ( Small effect I think. )
Machine tools: this "is" the industrial revolution. Lathes had been around for a long time, a "near modern" lathe, metal bed, cross slide, gear head - all the parts you need to start making screws in production, was mid 18th century, but "the pieces to make the pieces" were developed over centuries.
Cast iron, long history in China, not used in Europe until 15th century.
Windmills: came into use in Europe in the 11th and 12th century.
Not really important ( I think ) as waterwheels for pumping water and milling grain are pre-Roman.
So, there was much that slowly developed from 600AD, some in Europe, most in the east ( China, India, the Islamic world ( for lack of a better phrase )) that enabled the later developments.
So, some foundation, better communication ( not lots faster, but broader ), and a political environment of semi-constant conflict / competition between technological equals.
We've gotten a lot from NASA's research. They got a lot from the navy's.
As you mentioned, they had plenty of common things shared with the 18th century, but not with centuries before, that we take for granted today which can be considered technology.
To give some examples:
All roads were paved with marble which was an analog to modern concrete paving.
Homes in Crete and Pompeii have been found with Glass Windows.
Aqueducts carried fresh clean water and home sewerage was freely available.
Propaganda and even advertisements were plastered in the wall.
A full electoral and democratic system was in place, similar to the constitutional monarchies of the late 18th.
Carriages were modern, structured and a full profession was set to tend them and care for them.
All public plazas and city streets were illuminated at night using several types of oil lamps
Intercity communication was accomplished by a structured system led by the Military which was organized and heavily equipped.
Reading and writing was common place and a detailed calendar was used.
Scientific schools and libraries were heavily maintained and most knowledge was open sourced.
Public performances and (some) freedom of expression was carried out.
So yes, they didn't have planes, trains nor automobiles, but remember that all of these required a prolonged time of peace and stability which couldn't be achieved until after the end of the Napoleonic wars and was broken by World War One.
So basically what happened was that the convoluted 18 century was followed a dramatic beginning of the 19th century, but once the ideas of the French Revolution took hold during the reign of Napoleon III and most of Europe was involved in the Spring of Nations, the liberal way of thinking prevailed and free enterprise transformed the monarchical Europe since the Middle Ages into the Modern Europe of the 19th Century, on the Roman side, the Empire started on the wrong foot with the intervention of Palestine in the 1st and 2nd Century.
Things literally went South when Christianity prevailed and the downward spiral ended with the divesture of the Empire in the 6th century. 1000 years had to pass for things to settle down and things could return to the "Old Normality".
The situation in the 18th century was very different. The 18th century had several breakthrough ideas and products that the Romans lacked: calculus, gunpowder, printing press, discovery of the Americas, magnetic compass and clocks, to name a few. But the biggest difference was the “scientific method”. The belief that you could decipher nature by observation, hypothesis and experiment. In Roman times, understanding of nature was only attempted by “logic”. Hence, Aristotle and other Greek philosophers were considered the experts and no one doubted them. You can’t have an Industrial Revolution without science. Engineering by itself isn’t enough.
OK, so we discovered gunpowder. In some other parts of the world, it had been known for a thousand yeard. We got magnetic compasses. Others had been using compasses for around a thousand years.
I am quite sure that the redskins discovered America long time before Columbus. Even long before Leiv Eriksson.
Mechanical devices for measuring time was known in the 13th century, even in Europe. Sundials was known in prehistoric times.