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Well, I think I've a response for this, but the situation in the Roman Empire was not too different from the 18 century in Europe, but curiously this did not lead to a Industrial Revolution, a knowledge explosion an so on. The reason, for me, was a tiny actor they lacked, one of the two main characters in computing.
What do you thing could be the reason?
Well some modern banks like Lloyd's made great part of his wealth from slavery, till late 18 century.
Some people could argue their job is slavery nowadays ...
Now seriously speaking, I think the actual reason was the lack of "0", half of our binary system.
This one came from India, like software stuff nowadays. I can´t image Oliver Heavyside building some foundations of engineering without a good supply of zeros.
Both the Greeks and Romans knew of the steam engine* for example, but they didn't use it (except to make the gods look more exciting) as slaves did a better job, cheaper.
They lacked the metallurgy needed to make the large pressure vessels needed for steam engines with useful power densities. At best they'd've been limited to low pressure models with performance ratings of IIRC less than a ton/horsepower that used so much coal they were only capable of being ran onsite at coal mines.
And the industrial revolution began using water wheels, so arguments pointing to the ancients not taking advantage of steam power are totally blaming the wrong thing to begin with.
Did you ever see history portrayed as an old man with a wise brow and pulseless heart, weighing all things in the balance of reason?
Is not rather the genius of history like an eternal, imploring maiden, full of fire, with a burning heart and flaming soul, humanly warm and humanly beautiful?
Training a telescope on one’s own belly button will only reveal lint. You like that? You go right on staring at it. I prefer looking at galaxies.
-- Sarah Hoyt
I think so. It came from India. Can you imagine the speed of light represented in roman digits?
Is is philoshopically interesting that an item devoid of existence, in fact it represents the opposite of existence, has such importance:
"Please, add some zeroes to my wage !!!"
"No,no the opposite side"
One of the things that seems to have made the industrial revolution so successful was developing machines to create machines.
It seems that if you can do this, you can then start to miniaturise and mass produce products with a similar quality.
Also the prior invention of the printing press meant that accurate information could be shared fairly easily.
“That which can be asserted without evidence, can be dismissed without evidence.”
If you're referring to "1" and "0", at low levels computers don't actually use ones and zeros, that's simply a modern mnemonic for representing two states. It is actually on or off, high or low, and can be represented by anything we want. They could have used "1" and "2", or "A" and "X", or even "+" and "-".
I think that's not the point, but a numerical system with or without zero.
For example. You can calculate the volume of a pool, or the weight of a rocket oxidizer easily in binary, hexadecimal o decimal system, both in metric or imperial, using a computer or a dirty piece of paper buy try to the same thing with romans. In you withdraw the zero from a numerical system, you wipe out all engineering, I think
Romans were pretty good engineers. There are aqueducts that maintain a steady 4 degree angle, even through tunnels. Not to mention things like the 100 foot unreinforced concrete dome over the Pantheon in Rome, which is still the largest of its kind, some 2000 years later.
I think if we were still using roman numerals, we would still be fine. We seem to be able to manage the calendar and all its weird and wonderful attributes. Speaking of which, Julius Caesar was able to reform the calendar in 46 BC, to within 99.99% of the tropical year. That's pretty good calculations for a number system without a zero, I'd say.
They pushed its numerical system to its limits, no doubt, and got got incredible things.
But if you withdraw the zero of many of out engineering fields things like the Fourier Transform get really complicated.
As another example, it is predict the planets position with the middle ages earth centered system. but if you place the sun in the center, things became simpler.