http://terrytao.files.wordpress.com/2010/10/cosmic-distance-...
I feel like these days, we aren't putting in as much effort in these endeavours as the days of old. I wonder why...
In some ways, the wasted educations and wasted talent of today is apalling. I was in the Sainte Chapelle in Paris recently and realized no one has created anything like it in 800 years.
What I found most fascinating about the explanations (I was in pre-calc at school at the time) was the math involved. During my classes (or any math class I've ever been in) they gave us formulas and equations but no meaning or real world context. If they'd told us how we could use the distance and angles to figure out what they'd figured out so long ago I think the math would have been much more interesting and brought home the point of why it is relevant to anything.
https://github.com/lifeisstillgood/importantexperiments4kids
I think I can get support for something like this from STEMAmbassadors of the UK. I shall see.
Comments?
The method of Aristarchus is much more clever than that. At 1/2 moon, the earth/moon/sun forms a right angle. The angle moon/earth/sun could be measured as about 3 degrees - something that the ancient Greeks could measure. This gives a ratio of earth-moon/sun-moon distances between 18 and 20.
Then during a lunar eclipse, you can measure the width of the cone of the earth's shadow vs. the moon's width. During a solar eclipse you can see that the moon's angular width is about that of the sun. That information, plus the measured radius of the earth, and a bit of geometry, gives you an estimate of the size of the moon.
http://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_%28A...
Having said that, I am personally fascinated by history during this time as it led to the genesis of a lot of our current nation states and the very paucity of the historical record from these times just adds to the romance for me!
Perhaps more important was the Sui/Tang dynasties in China around 600 AD kicking off over 1000 yrs of being the most developed place on Earth. They built the Grand Canal connecting the Yellow and Yangtse rivers, turning them into a single economy based on trading rice for coal.
The hard part isn't really the basic scientific discoveries. It's the society-wide political and economic conditions that let capital accumulation go exponential.
The ancient Greeks had working toy steam engines. They could have started the industrial revolution right there. Why didn't they? There are lots of theories. Maybe they hadn't invented good enough ideas about banking and property. Maybe their reliance on slave labor blinded them to the value of mechanization. Maybe their class system kept people with scientific knowledge too far away from people with practical working knowledge.
The bottom line is that scientific knowledge is probably not the limiting factor.