In 200 B.C. Eratosthenes showed that the earth is round and calculated it's circumference by means of an experiment. However:
How did Eratosthenes know that b) was the case and not a)?
I tried looking it up, the two answers I found were basically:
>they already suspected that the earth was round
or
>it was common knowledge at the time that the sun's rays that hit earth are (roughly) parallel
If the first, how could they argue against a), if the second, how did they know that?
>if the second, how did they know that?
That can be observed from anything that emits light. But you are right at some level. Technically they could not have been 100% sure because they had shit lighting like fires unlike the controlled lighting we have today.
This is simply a case of a genius' intuition saving the day. They had no way of 100% knowing that the rays were parallel but as Erastosthenes wasn't a fucking brainlet he knew exactly what was happening.
If your IQ is less than 160 you may not comprehend this notion of intuition but trust me, it works.
>trust me, it works
I thought this was Veeky Forums desu
>That can be observed from anything that emits light
... but the rays aren't parallel, no? They only appear that way because of how far away the sun is. So basically the question is, how did he know the sun was so far away?
>Science has no place for intuition
>I thought this was Veeky Forums desu
Yeah and you are asking a historic question which begs the question why the fuck aren't you on Veeky Forums?
>how did he know the sun was so far away?
INTUITION
NTUITIONI
TUITIONIN
UITIONINT
ITIONINTU
TIONINTUI
IONINTUIT
ONINTUITI
NINTUITIO
Brainlets would never understand.
That's not what I'm saying. "Just trust me on this" is how magic works, in science you should be able to explain it, no? Intuition might give you a hunch, but it's not a proof
>geometry isn't science if it happened in the past
>INTUITION
Calm down on the autism. Intuition isn't proof. So you're saying he really didn't know and was just making an assumption that turned out to be correct, though he couldn't justify it to anyone else at the time?
>So you're saying he really didn't know
No, I was clear on what I said. You can't observe this property of light by simply looking at anything that emits it. But I said that objectively, there was no way of 100% being sure because they only had natural lighting so they couldn't really do an experiment that confirmed it.
We can today but back then they had to take their inferior observations and their intuition.
>was just making an assumption that turned out to be correct, though he couldn't justify it to anyone else at the time?
Almost. But as you outline in your diagram, there are only two sensible possibilities. But as Erathostenes had the goal of finding the shape of the earth with this experiment, it is clear why he would choose the round-earth option. But after that he had to convince other people, otherwise his experiment would not be famous. He probably did justify to everyone, but it is just that his justifications are not to our standards today.
The only no-bullshit explanation is that he was really smart and his intuition guided him well.
A wouldn't give consistent results throughout the day like B. In A, the rays would become more divergent when it was closer to mid day, whereas they would stay equally divergent in B.
This is based on my own intuition, I'm not sure if this would be observable or was the case.
Camera obscura was known about then & Euclid knew light travelled in straight lines in 300BCE so it's fairly easy to suggest that far away light sources have rays that appear parallel
>You can't observe this property of light by simply looking at anything that emits it.
>That can be observed from anything that emits light.
I assume you mean can and not can't there?
If so, again: which property? That the rays are basically parallel if the light source is far enough away? If so, that's not the problem, it's clear to me that you can easily observe this.
The question is then simply, how did he know that the sun was far enough away that he could consider the rays hitting Alexandria to be parallel to those hitting Syene?
>He probably did justify to everyone, but it is just that his justifications are not to our standards today.
Right, but what I get from your post is "He was just really smart and knew, you brainlet", which wouldn't hold up at the time either.
Could you specify why, or what you mean by more divergent? In which direction, that is?
>far away light sources have rays that appear parallel
Right, in both models the light is traveling in straight lines. Like I said above, the question is, I guess, on what basis did he assume that the sun was so far away that he could consider the rays hitting Alexandria to be parallel to those in Syene?