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The Forgotten Revolution

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47 pointsamadeuspagel19 comments

Some more examples can be found in Schrodingers book "Nature and the Greeks".

One that stuck with me is the "discovery" of atoms. Some philosopher (don't remember the name) in Greece was thinking about the volume of a pyramid. And he imagined what would happen if we dissected the pyramid through the middle and looked at two squares formed on the bases. He reasoned that the squares should have equal areas, however if that was the case for every such dissection the pyramid would never form and instead we would have a cube.

So his reasoning was that in order to explain this paradox objects in the real world should be composed of small elements, so that after dissection the squares are slightly different.

The same argument could be made for atomic divisions of time à la Achilles and the Tortoise, aka Zeno's paradox. However is time atomic?

The argument is "faulty" because it does not take into account infinitesimally small differences. E.g. like dx in integrals.

When you divide a time interval in two, you don’t get any cross section whose size you could base the argument on. Even if you would get a cross section, time arguably would be more like a cylinder or prism than a pyramid.

Horizontally. The square forming the new base of the upper segment, and the square forming the new top of the lower segment. They should be the same size, but if they were the Pyramid couldn't taper smaller and smaller towards the top, so the lower face needs to be a few 'elements' more diminutive. .. of course it would depend if you cut it in half between two stone layers, or half way through one stone layer, and if your cut lined up with the top or bottom of the kings chamber or not.

Could it have been Lucretius?

Lucretius was a roman philosopher, who, according to the book that this article refers to was inspired by greek philosophers.

Indiscrete Thoughts by Gian-Carlo Rota is full of this sort of thing [1]. In fact he made me see mathematics as a unique domain that escapes both empiricism and rationalism. It's real and out there to be discovered timelessly by each civilisation, and yet we make it all up as we go along. There's nothing new under the sun - except the next thing you can imagine.

[1] https://www.goodreads.com/author/list/345801.Gian_Carlo_Rota

That struck me too, but also interesting that the myth of heavy objects falling faster was understood to be false back then too, and that they might have had a grasp of gravity before Newton.

Everybody knows that Aristotle – and thus “the Greeks” – thought that heavy objects fall faster than light ones. Supposedly it took Galileo to prove him wrong. But in fact there is a clear statement in Lucretius (De Rerum Natura II:225-239) that objects of different weight fall at the same speed, unless air resistance kicks in;

"Russo argues that scientific progress largely came to an end by 150 BCE, and the Roman period saw an actual decline in scientific understanding."

Off topic, but apparently something similar happened in China, at roughly the same dates. The era of innovation was surprisingly early, and it was over before these civilizations reached their material peak. I just read this book:

https://www.amazon.com/gp/product/1936166755/ref=ppx_yo_dt_b...

This focuses on the political debate, which in some ways measures the extent of the intellectual awakening. It truly shifted my perspective about the depth of political debate in China. Apparently the lead up to the Warring States Periods, and then the Warring States Period itself, caused the greatest political debate that had existed anywhere in the world up to that point. Almost every idea was put forward: liberalism, authoritarianism, totalitarianism, constitutionally limited monarchy, centralization of the economy, decentralization of the economy, primitivism but then also some praise of the benefits of specialization and the use of economic elites. Each state was trying to win the popularity contest, and various princes occasionally tried very liberal government to win over the populace to contribute more to the war effort.

And this whole era came to a sudden end in 221 BC, when Chin was victorious in uniting all of China. But before that, China had seen an incredible intellectual awakening.

The point is, in Europe and China, the era of intense intellectual activity happened centuries before the imperial consolidation, and centuries before the material peak of the classical era.

i suspect economic shifts due to the wars made this happen in china and in greece.

having a job is nice and all, but when you can just do ~whatever~ instead, innovation-magic happens.

Ancient Greeks also made basic steam engine as well as basic rail transport. The limiting factor was probably metallurgy, but it's fun to think about what-ifs.

What would they do with a steam engine, even if a practical one was built? Mines could usually be kept clear using hand pumps, and there was no coal mining then to make early engines useful. The many wars between Greek kingdoms resulted in thousands of skilled and unskilled laborers being pressed into slavery; a steam engine would also have to compete against that.

This article covers in detail how different the ancient economies were from 1700s Britain: https://acoup.blog/2022/08/26/collections-why-no-roman-indus...

Funnily enough they did use windmill pumps instead of steam for this exact purpose.

The thing with steam is that it clearly beats mechanical systems only at very high heat and pressure.

I would expect steam to have been used like in Korea - for heating efficiency.

Let’s create greekpunk. Like steampunk but with togas and sandals and temples, in a Mediterranean setting.

Not exactly the same, but try https://en.wikipedia.org/wiki/The_Years_of_Rice_and_Salt ?

I enjoyed it very much.

I thought the sequence was https://en.wikipedia.org/wiki/Catalan_number but its actually https://en.wikipedia.org/wiki/Schr%C3%B6der_number which is allowed to move diagonally.

I still can't see how the diagonal step comes in to the parenthesization.

No, it’s https://oeis.org/A001003 (super-Catalan numbers or little Schröder numbers), not https://oeis.org/A000108 (Catalan numbers) or https://oeis.org/A006318 (large Schröder numbers).

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