How was the size of Earth first measured? (2015)

pages 156-158:

“Ironically, when Aristarchus proposed the heliocentric model, his contemporaries dismissed it, on the grounds that they did not observe any parallax effects...”

“ so the heliocentric model would have implied that the stars were an absurdly large distance away.”

“[Which, of course, they are.]”

Why are Pyramids the first evidence of Earth’s measurements?

This is an unfortunately very uniform problem with "school", I'd say (in the US system / nomenclature) from about post-elementary up to "undergrad". Too much of the junior high school and high school classes end up as "piles of facts". The vast majority of attempts to improve education* never deal with this underlying issue, and, thus tend to just make the problem even worse. (Most likely, for various reasons including 'difficulty', attempts are made to avoid this issue.)

You can impose any standards you want - if all you're training on and testing for is ~regurgitation of facts, that's what's going to be optimized for - all of the forces at play will push even the best of teachers (those who might try to provide something other than the driest most immediate-term "goal-oriented" course / experience) towards this terrible (minimum) "standard".

At this point, I highly doubt this will ever be fixed - and certainly, can't see that happening in my lifetime. In the past few decades, hostility, and outright MARKETING of hostility, towards education has increased dramatically. Education is perennially underfunded and massively inequitable from locality to locality (and at even "finer grained" levels). Most of the fights around education these days are so far removed from questions of SERVICE and ARE WE DOING THE BEST WE CAN FOR FUTURE GENERATIONS? that there's just no way to imagine any serious or appropriate attempt can be made to address the real inadequacies of our recent & current system.

It's truly a shame. We'd all be far better off if there was more investment in, respect for, etc. education, teachers, STUDENTS (our kids), etc. Partly, this is a generational issue that even gets at the voting power of generations ... It is possible that Gen X, in part by being a smaller "generation" and in part because of their own experiences of being comparatively ignored and pushed to the side by the priorities of other generations [particularly, the older generations] across their own "lifecycles", will actually help swing things back a little towards student-oriented service (so-to-speak). But, I'm not 'optimistic' either regarding intention or, even more so, actual action.

It's a kind of tragedy, blasting people IN THEIR FORMATIVE YEARS with piles of facts in such a way as to kill off INTEREST and the possibility of real UNDERSTANDING, guaranteeing we end up with a far less informed, engaged, and healthy COMMUNITY and PEOPLE than we might otherwise have.

* Most, seemingly, quite ill-advised, unfortunately. Ill-advised based on research and the experiences of people who have spent years studying (sometimes, even, with a methodical empiricism!) "pedagogy" and "child psychology", and those who have worked on and refined models that tend to have real advantages (e.g., "Montessori" comes to mind - the data is mixed but generally supportive of the benefits of this comparatively grounded in science method, see, e.g., https://www.nature.com/articles/s41539-017-0012-7). Part of this is because of various "stakeholders" engaging in the usual tug-of-war BS where only lip-service is paid to the actual target population this essential SERVICE is supposed to be CENTERED ON...

Downvoted, but valid.

I would claim that Ugg’s effort counts as a lower bound on the size of the Earth, and is therefore a legitimate constraint on true measurement. This bound might even be sufficient for some purposes.

It also seems like ancient mariners should have been able to use the visible arc of the horizon to get a rough guess, long before Eratosthenes.

All we are really arguing about is, how good are the error bars?

This article had one detail that was not included in the video that had always bugged me. Carl says "how could it be .. that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria". That seemingly requires coordination between 2 people across a vast distance and accurate time measurement. I rationalized that it could be accomplished with people at each location, each with a sundial, making records of shadow length, and later comparing their measurements, but it still seemed like a messy explanation.

The detail of no shadow at the zenith on a specific day solves that problem. That removes the complication of the coordination of 2 observers and the lighting of the well better explains why the phenomenon was noticed to begin with.

The other unresolved problem for me is that it still requires the assumption that light is parallel i.e. the sun is (relatively) incomprehensibly far away, and that was not established fact at the time afaik.