How do we know what we know?

In astronomy, there's a commonly used phrase: “we stand on the shoulders of giants,” part of a longer quote sometimes attributed to Isaac Newton, although I'm not sure that he was ever humble enough to say something along these lines. The entire quote is: "If I have seen further, it is because I stand upon the shoulders of giants."

Who are those giants Newton stood upon? Truly too many to name, but they were thinkers, geometers, astronomers, mathematicians, and natural philosophers who thought deeply about the nature of the universe and our own place within it. Each of them derived a small part of the whole, or in some truly prodigious cases, multiple parts of the whole of our knowledge about how we exist in the universe today. Newton's contributions were many, including his laws of motion and gravity as a concept that could be studied and applied. But in order to understand that our Earth is round, how big it is, and how far it is from the Sun, we can turn our eyes to centuries before Newton's birth and several hundred kilometers to the south, in Greece.

It's hard to say who initially proved the Earth is round, as anyone who sat and thought about a lunar eclipse long enough would surely come to that conclusion. Likewise, watching a ship sail away from your position on the coast means that eventually, the sail of that ship dips below the horizon. Either of these are strong proofs to the thinking person that our world is round. But to offer our Flat Earth compatriots a bone, it certainly does seem flat on a local scale. When I rest a basketball upon what seems to be flat ground, it does not roll away, but this does not mean that the world in its entirety is flat. Each of the bumps on the surface of that basketball seems to be on a flat surface; a large sphere seems to be flat at a small enough scale. To understand why our world seems flat, it's important to understand how large our world truly is. For that work, we turn to Eratosthenes of Cyrene.

A friend once told me that the real words of scientific discovery are not “Eureka” but “huh, that's weird.” I think this underscores a very valuable point: observing something unusual and trying to understand what's going on can lead you to some very interesting discoveries. In the Egyptian city of Syene, it was known that there was a well that had the sunshine straight down it, illuminating it in its entirety at noon on a specific date, June 20th. To someone else, this could have been an unusual characteristic of that well, but to a person who was noticing the unusual and paying attention, it became a valuable piece of apparatus. This well became a very accurate indicator of exactly where the sun is in the sky, and by measuring a good distance away from that well from where he was currently working in Alexandria, Eratosthenes came up with a way of measuring the circumference of the Earth. By measuring the shadow cast from the height of a known object (in this case, an obelisk acted as his gnomon), he could tell the angular difference between the well in Syene and Alexandria. By comparing that to the measured distance between the two cities, he could figure out the comparative distance. The change in angle between the well and the obelisk compared to the entirety of a circle equals the change in distance between the two cities compared to the circumference of the globe. This very clever proof allowed for a surprisingly accurate estimation of the size of our own planet Earth.

More to come!