Flat Earth Versus Spherical Earth

In the Smoky Drinky Bar on Saturday night, Gráinne was arguing in favour of a Flat Earth with Brigitte and myself (conversations like these only ever happen in the Smoky Drinky Bar).

Never having had to argue against a Flat Earth, I cast around for evidence against it. What about the view from outer space? “Photoshopped,” said Gráinne. And who knows, perhaps it was? After all, I’ve never been to outer space. What about the view of the Earth from an airliner 10 km high? Didn’t the horizon have a visible curve? “An illusion,” Gráinne replied.

Eventually I fell back on my own maritime experience of seeing ships hull down below the horizon (or, same thing, the disc of the setting sun vanishing below the horizon). I even dug up a video of a ship hull down:

But afterwards it occurred to me that Gráinne could have dismissed this as well. She could have said that what we were seeing here was a submerged or sunken ship.

Since Saturday night, I’ve continued to think about ways of proving that the Earth is round. This morning I began thinking about how a little archipelago of islands might easily be visible from each other. How far was it possible to see out across the sea on a spherical Earth?

I used the Theorem of Pythagoras to work this out. If the spherical Earth has a radius R, and an island rises a height H above the surface of the Earth, how far is the distance D to the horizon, as seen from the top of the island? The answer, with a spherical Earth of radius 6371 km was that the distance to the horizon from an island of height H km above sea level is about 113√H km. So from an island 10 metres above sea level you can see 11 km, and from an island 100 metres high you can see 35 km, and from an island 1000 metres high, you can see 113 km.

Since  I was thinking about an archipelago of rocky islands, like those in Greece, I wondered if it might be possible for some Greek islands to be seen from the tops of nearby islands.

Using Google Maps, I soon found that the highest point on the island of Milos was 730 m. So, using my horizon distance formula, this meant that it was possible to see for 95 km in all directions. Plotting that circle on a map, I was astonished to find that from the Prophet Elias on Milos it was possible to see 12 or more other Greek islands. And from the top of a 1000 m high mountain (Mount Hymettus) just a little southeast of Athens, it was possible to see 113 km in all directions:

Furthermore, because the two circles overlapped, it meant that from the top of the mountain near Athens, on a clear day it was possible to see the top of the Prophet Elias on Milos.

And that meant that it was possible to communicate very quickly between Athens and Milos, using fires by night, and mirrors by day. And since in antiquity, unlike now, there were probably plenty of clear days, that would have meant that communication between all the Greek islands would have been very rapid. And this rapid communication would have extended to Crete, in the centre of which stands the 2,456 m high Mount Ida, from which Milos would also have been visible. It may have taken the Ancient Greeks many days of sailing or rowing to actually go from one island to the next, but communication between the islands would have been very fast. A short message like “Persian fleet near Karpathos” could have been flashed to every Greek island in the Aegean Sea within hours of the fleet being spotted. No wonder Greece was made up of a league of lots of tiny states.

It also struck me that, given the unique topography of the Aegean, the Greeks were ideally placed to be able to see that, while some nearby islands were visible to them, and not others, the Earth (or rather the sea) had to be curved. If the Earth and the sea was flat, all the islands should have been visible from each other. It was probably possible for them, using geometry, to work out how how far each island was distant from the others.  And they could also have used geometry to find out how high the highest point on each island stood above sea level. So, going back to my Pythagoras equation, if they knew H and D, they could also find R, the radius of the Earth.

And of course Pythagoras was Greek, and so was Aristarchus of Samos (shown with balloon near the coast of Turkey) who not only knew about the sphericity of the Earth, but also that the Earth went round the Sun, 2000 years before Copernicus. And the Greeks were probably great geometers because of where they lived.  In other countries, with the view obscured by hills and mountains, there was no such natural laboratory as the Greeks had in which to conduct geometrical investigations over long distances.

I then extended my investigations to the rest of the Mediterranean.

Here I found, again to my surprise, that it was possible, using one or two intervening islands (like Pantellaria and the Galite islands), to quickly communicate between Tunisia and Sardinia and Sicily. And also to communicate between Corsica and Italy and France. And this meant that the sea-going Carthaginians in what is now Tunisia also had fast communication channels by which they could control the western Mediterranean.

And all this spun out of a good-natured conversation with Gráinne.

P.S. I could have got the math wrong, of course.

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About Frank Davis

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40 Responses to Flat Earth Versus Spherical Earth

  1. garyk30 says:

    What was the ‘proof’ for the Earth being flat?

    • Frank Davis says:

      Gráinne’s? She didn’t offer a proof. She dared us instead to prove that it wasn’t flat. Which was why I kept coming up with various arguments in favour of a spherical earth.

      Her view was that water found a flat level, So the sea had to be flat as well. And if you had a powerful enough telescope, you’d be able to see things a very long way away. When I told her that, in crossing the Atlantic ocean at age 10, I’d often seen ships hull down below the horizon, she said that it was a long time ago, and my memory was probably playing tricks on me, and I hadn’t really seen any such thing. That was when I found the YouTube video showing a ship hull down.

      I found a Popular Science website that showed 10 easy ways you can tell for yourself that the Earth is not flat.. But I didn’t think most of them were much good, because they largely relied upon secondhand information (hearsay) like photos supposedly taken from outer space. And when was the last time that I saw an eclipse? It’s not easy to readily disprove the Flat Earth theory.

      • I always enjoy when people claim something and rather than having any real proof, simply challenge you to disprove it. I liked your post – very interesting little snippet of how civilizations advance or hold advantage over their space.

        While I love alternative theories of the “official story”, and even believe a few of them, I’ve never seen or heard of any good argument for a flat earth – actually I think the whole notion is rather comical in this day and age. When I was studying architecture, there was a whole lecture dedicated to one of the largest buildings in the world (in terms of coverage) which is a Boeing facility in Everett Washington (where the 747 is produced). Apparently it is so large that the columns that support the roof aren’t parallel to each other (at the far ends) as they’re plumb to earth and the curvature makes them slightly skewed away from each other at the top. I’m guessing it’s a very small deviation, but fascinating.

        It got into a bit of a tangent about how nothing is really ‘planar’ or straight in reality, yet geometry is ‘good enough’ to do what we need it to do.

  2. George Speller says:

    I remember on a very still night standing in tje cockpit of a boat, looking at a lighthouse some 20 miles away. When I sat down it disappeared. I tried this a few times, and had never before seen such a good example of the curvature.

    • Frank Davis says:

      That’s an interesting one. Assuming you were 2 metres (0.002 km) above sea level in the cockpit of the boat, then according to my formula your horizon would have been 5 km away. And when you sat down (green) it was probably less than 1 km away

      You had to be just the right distance from the lighthouse for that to happen.

    • RdM says:

      In earlier times, this was explained away as a trick of perspective…
      http://www.sacred-texts.com/earth/za/za32.htm

      • Frank Davis says:

        3.–Any distinctive part of a receding body will be-come invisible before the whole or any larger part of the same body.

        Quite so. But the largest and most distinctive part of a ship is its hull. So why does that disappear, and not the thin spindly masts mounted on it?

        • RdM says:

          Indeed. I wasn’t saying I believed it.
          Just pointing out what was thought earlier.
          As I’m sure you understand, probably no need to say.

  3. beobrigitte says:

    Finally I get a word in! :)
    I tried to mention airplane flights in the conversation…. I do know that a flight from Frankfurt (Germany) to Vancouver (Canada) takes 9 hours only when the plane (as they do) fly over the arctic.
    A flight from Amsterdam to Boston takes 8 1/2 hours, route is flying near Iceland.
    On a flat earth these flying times would not make sense, considering Boston being on the east coast and Vancouver being further north on the west coast of North America, would it?

    • Frank Davis says:

      Flying times also depend on wind speeds.

      The same is true for the exact same route going in one direction or other. For example sailing from America to Europe was usually quite rapid (about a week), but sailing from Europe to America could take 3 weeks or more.

      • beobrigitte says:

        Work it out on a flat earth with the arctic in the middle. Even the variations in flying times (head wind accounts at the flights mentioned for about at most 1 hour) don’t match a flat earth.
        Also, long haul flights have a pretty much set flying speed, so speed is not an issue.

  4. Frank Davis says:

    The Colossus of Rhodes is reported to have been 33 m high, and stood on a marble base 15 m high, making it 48 m high in total. So according to my formula, its light would have been visible 25 km away. I used Google maps to show this distance.

    It meant that the lighthouse would have been visible all the way across the strait between Rhodes and Turkey.

    If the Colossus had several lights of different colours at different heights, it might have been possible to use it to gauge how far distant one’s ship was from it.

    The Pharos of Alexandria is estimated to have been 137 m high, at maximum. That meant it could be seen up to 42 km away.

  5. garyk30 says:

    “Her view was that water found a flat level, So the sea had to be flat as well.”

    If the Earth was flat, the oceans would just drain off over the edge.

    Thus, the Earth must be round.

  6. C.F. Apollyon says:


    Excellent stuff Frank. Thanks. <3

  7. beobrigitte says:

    In the Smoky Drinky Bar on Saturday night, Gráinne was arguing in favour of a Flat Earth with Brigitte and myself (conversations like these only ever happen in the Smoky Drinky Bar).
    They sure do!!! (Remember the funny game I won? hehehehe) Perhaps we have so much variation of topics simply because the group of people stay together; no-one leaves for a cigarette? We smoke as we talk and talk about anything and everything.
    I’m sure Grainne played the devil’s advocate – surely she would have checked passenger flight times to different points on this planet to see that the spherical nature of this planet is being used to transport advantages. Never mind, we had a few hours good discussion and when I – as the last one – was logging out, I was signalled Bucko had logged in. So I logged back in and had at least another hour or so of fun with Mr. and Mrs. Bucko.
    Actually, so much for an early night…. Was gabbing to RDM until now and it’s going to take an hour to sort some stuff for my next travel on Saterdy…. Never mind.

    Anyone disproving the passenger flight times, I’m all ear. No calculation needed, just check on departure, arrival and route. Easily done.

    • Rose says:

      Brigitte
      You are flying on Saturday? Please take some Twiglets and see how you get on, Junican said that he didn’t have the desire for a cigarette the whole time, But dissolve the yeast extract on your tongue before you crunch up the biscuit.

      You know how sublingual application works, but for the benefit of others –

      How the Taste Bud Translates Between Tongue and Brain
      1992

      “However, taste researchers now know that the end result is a series of micro-electric currents, induced by nerve-cell messenger chemicals or direct interaction of taste stimuli with taste-cell membranes, that tell the brain what the tongue has experienced less than a moment ago”
      New York Times

      • beobrigitte says:

        Brigitte You are flying on Saturday? Please take some Twiglets and see how you get on,
        I’m only on a short flight, but in May I have a long haul flight. Will definitely take twiglets with me then!

        • Rose says:

          Thank you, Brigitte, I’d suggest that you buy the smallest bag you can find because just a few keep working for ages.

  8. waltc says:

    Well, it certainly proves that you can’t reason people out of their vested convictions, and proves the other thesis that annoying yhem with facts just hardens their position. I suppose she could explain why nothing ever fell over the edge? But here, of course, is the definitive counter argument:

    https://me.me/i/if-the-earth-was-flat-cats-would-have-pushed-everything-13749754

  9. smokingscot says:

    O/T

    Nice to see the chap chosen by the WHO (and subsequently dropped) as their ambassador in Africa has – at long last been deposed as Zimbabwe “transitions”.

    http://www.express.co.uk/news/world/879724/Zimbabwe-Robert-Mugabe-coup-ZANU-PDF-Party-army-military-Emmerson-Mnangagwa

    Hopefully this one’ll stick. No repeat of the Turkey disaster. Erdagon had a field day killing and jailing. Shudder to think what Mugabe and his brutes will do if they ever get back.

    (First priority – get a hold of all their bank accounts).

  10. RdM says:

    Malagabay noted last year that NASA’s tsunami simulations fitted a flat earth better.
    Although otherwise neutral in comment.
    https://malagabay.wordpress.com/2016/01/01/the-flat-earth-and-sea-level/

    I first became aware of the flat earth theory as a schoolboy, listening in the early 60’s to Peter Sellers, on one of my first records… a satiric scoffing take on it, so perhaps I’m biased…
    I found recently an EP of his with most of what I remember on it, but not this track, remastered:

    Fullers Earth

    Worth a laugh?

  11. RdM says:

    Plotting that circle on a map, I was astonished to find that from the Prophet Elias on Milos it was possible to see 12 or more other Greek islands. And from the top of a 1000 m high mountain (Mount Hymettus) just a little southeast of Athens, it was possible to see 113 km in all directions:

    Furthermore, because the two circles overlapped, it meant that from the top of the mountain near Athens, on a clear day it was possible to see the top of the Prophet Elias on Milos.

    I’m sorry, I can’t see this… as a proposition.
    Just because the circles of vision of each happen to overlap, it doesn’t magically extend the field of vision all the way from one to the full extent of the other.

    No, each can see just as far as each can see.
    Someone in the overlap might see both.

    P.S. I could have got the math wrong, of course.

    Perhaps the above was in the nature of a trick question, to see who was awake?

    Cheers!

    • RdM says:

      I might be wrong myself, of course…

    • Frank Davis says:

      I’m sorry, I can’t see this… as a proposition. Just because the circles of vision of each happen to overlap, it doesn’t magically extend the field of vision all the way from one to the full extent of the other.

      I need only employ the diagram I used upthread in responding to George Speller:

      Here the maximum extent of the light from the lighthouse is 27 km, and the furthest that George Speller in his boat could see was 5 km. It’s just possible for the light from the lighthouse to pass just over the the surface of the Earth and be seen by George Speller 32 km away. And if there was another lighthouse of the same height 22 (27 – 5) km further away from the first one than George Speller, the two light houses would just be able to see each other’s lights, while being 54 km apart. For the light doesn’t stop 27 km from the lighthouses: the light that doesn’t strike the sea carries on over the top of it.

      • junican says:

        Put another way, you would be able to see a man in the crows nest of another ship from the crows nest of your ship, but neither of you would be able to see the decks of the ships.

      • RdM says:

        Thanks Frank and Junican (putting it another way) for your responses.
        Somehow this didn’t seem obvious at midnight after a surfeit of stout…
        I’m glad I asked then though, else I might have still been wondering.

  12. RdM says:

    And all this spun out of a good-natured conversation with Gráinne

    I’m glad it was good-natured, as I’m sure it would be, even only having seen Gráinne a couple of times… I seem to have missed some great conversations, perhaps after having to leave under a slight cloud with flaky wi-fi… I hope I have fixed that now with a new router and downloading a wifi-analyser app… and am still pursuing installing linux on a much smarter laptop with 1GB ethernet afforded by said new router instead of the old 100MB ethernet, and upgraded cables… so that hopefully I will no longer be accused of disrupting the experience! ;=})

    Anyway, it took me some time to find again, an image from a Scientific American article I linked to in a comment back in The Spiral Of Silence, which seemed appropriate!

    All this might seem trivial compared to the profundity of your most recent post and comments, but I liked the image enough to want to find and present it again!

    Cheers!

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