Opinionated History of Mathematics
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History of mathematics research with iconoclastic madcap twists.Read more »
History of mathematics research with iconoclastic madcap twists.
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Societal role of geometry in early civilisations
3 days ago
·
36 minutes
In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical technocrats were deployed to settle conflicts regarding taxes, trade contracts, and inheritance. Mathematics enabled states to develop civil branches of government instead of relying on force and violence. Mathematics enabled complex economies in which people could count on technically competent administration and an objective justice system.
Transcript
How did geometry start? Who was doing it, and why, in early civilisations? The Greeks invented theorem and proof, but long before them there was geometry in Egypt and Mesopotamia. So that’s practical geometry, applied geometry.
Or is it? Actually even the oldest sources have lots of pseudoapplications in them. Such as: Find the sides of a rectangular field if you know the perimeter and the diagonal. Or: I have two fields, and I know how much grain each field produces per unit area, and I know the total grain produced by both of them, and I know the difference between their areas, now tell me how to find the area of each field.
Not the kind of situations you find yourself in every day exactly. You can judge for yourself if that deserves to be called applied mathematics. Given obscure and convoluted information, find something that should have been much easier to measure directly than this artificial data you somehow had access to.
In any case, geometry like that, whatever you want to call it, was highly developed almost four thousand years ago. Why? What made people do this? Let’s try to find out.
Early mathematics emerged where there was fertile soil. Rivers that made this possible. Agricultural abundance meant resources enough to expend some people specialising in mathematics instead of having all hands on the ploughs.
Look at a modern population density map of Egypt. You will find that virtually the entire population is concentrated along the Nile; all the rest is pretty much desert. That’s still today. Even with the assistance of modern technologies the river area is by far the most liveable. Even more so back then when geometry started, thousands of years ago.
It was the same in Mesopotamia, presentday Iraq. Also a river civilisation with very good agricultural conditions. They had legendary gardens that were praised in ancient sources. Google it: The Hanging Gardens of Babylon. You will see some nice pictures of what these luxurious gardens might have looked like. That’s a nice visual for this idea that it was agricultural abundance that made a specialised pursuit like mathematics possible in those societies.
So that explains why they had the resources to support mathematics. But why would they want to? What did they stand to gain from geometry?
Basically, mathematics was for a long time about commerce and taxes; bureaucratic management of workers and produce; inheritance law. Those kinds of things.
Eleanor Robson’s book is very illuminating about this. “Mathematics in Ancient Iraq: A So...
Read more »
In ancient Mesopotamia and Egypt, mathematics meant law and order. Specialised mathematical technocrats were deployed to settle conflicts regarding taxes, trade contracts, and inheritance. Mathematics enabled states to develop civil branches of government instead of relying on force and violence. Mathematics enabled complex economies in which people could count on technically competent administration and an objective justice system.
Transcript
How did geometry start? Who was doing it, and why, in early civilisations? The Greeks invented theorem and proof, but long before them there was geometry in Egypt and Mesopotamia. So that’s practical geometry, applied geometry.
Or is it? Actually even the oldest sources have lots of pseudoapplications in them. Such as: Find the sides of a rectangular field if you know the perimeter and the diagonal. Or: I have two fields, and I know how much grain each field produces per unit area, and I know the total grain produced by both of them, and I know the difference between their areas, now tell me how to find the area of each field.
Not the kind of situations you find yourself in every day exactly. You can judge for yourself if that deserves to be called applied mathematics. Given obscure and convoluted information, find something that should have been much easier to measure directly than this artificial data you somehow had access to.
In any case, geometry like that, whatever you want to call it, was highly developed almost four thousand years ago. Why? What made people do this? Let’s try to find out.
Early mathematics emerged where there was fertile soil. Rivers that made this possible. Agricultural abundance meant resources enough to expend some people specialising in mathematics instead of having all hands on the ploughs.
Look at a modern population density map of Egypt. You will find that virtually the entire population is concentrated along the Nile; all the rest is pretty much desert. That’s still today. Even with the assistance of modern technologies the river area is by far the most liveable. Even more so back then when geometry started, thousands of years ago.
It was the same in Mesopotamia, presentday Iraq. Also a river civilisation with very good agricultural conditions. They had legendary gardens that were praised in ancient sources. Google it: The Hanging Gardens of Babylon. You will see some nice pictures of what these luxurious gardens might have looked like. That’s a nice visual for this idea that it was agricultural abundance that made a specialised pursuit like mathematics possible in those societies.
So that explains why they had the resources to support mathematics. But why would they want to? What did they stand to gain from geometry?
Basically, mathematics was for a long time about commerce and taxes; bureaucratic management of workers and produce; inheritance law. Those kinds of things.
Eleanor Robson’s book is very illuminating about this. “Mathematics in Ancient Iraq: A So...
Read less
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