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    Celestial navigation and the spherical Earth
    From: Frank Reed
    Date: 2018 Jul 29, 22:36 -0700

    There's a lot of online craziness over the roundness of the Earth. And much of it comes from people getting roped in by trolls who really know better. Those roped in scream and rant, "How could anyone not believe that the Earth is round?!" In fact, for most people, it's a matter of faith --faith in the state of knowledge. It's an interesting issue. They don't know much more than a hint of the real science --it's just "one of those things" that everyone knows.

    For at least some of those people, there is a genuinely interesting epistemological question here (epistemology is a long word for a simple question: "how do we know what we believe we know?"). Can any of us really prove that the earth is round with one simple, irrefutable observation? Well, no, because that's not how science develops. But among the many observational pieces of evidence available, by far the best is our own subject: traditional navigation and the match between celestial navigation and dead reckoning distances. The angles of celestial navigation would not align with the distances run as measured by dead reckoning if the Earth deviated significantly from a spherical shape. I can measure an angle between two stars at my observatory in Britain, and then I can sail from the spot where one star is straight up to the spot where the second is straight up and (accounting for the earth's rotation), the distance travelled in degrees on the sea will match the angle measured at the observatory within a reasonable margin of error. And this is true for every pair of stars whose angular separation I measure. This match between ground distances and angle on the sky works only on a nearly spherical globe. 

    I discovered tonight a rather unlikely source who knew this fundamental line of reasoning, at least in outline, and wrote about it over seventy years ago. It was George Orwell. Yes, that George Orwell --the author of Animal Farm and 1984 (well, not really "that" George Orwell since this was a pen name). And back in 1946, in a newspaper column, he wrote about the epistemological problem of "knowing" that the Earth is round:

    SOMEWHERE or other—I think it is in the preface to Saint Joan—Bernard Shaw remarks that we are more gullible and superstitious today than we were in the Middle Ages, and as an example of modern credulity he cites the widespread belief that the earth is round.  The average man, says Shaw, can advance not a single reason for thinking that the earth is round.  He merely swallows this theory because there is something about it that appeals to the twentieth-century mentality.

    Now, Shaw is exaggerating, but there is something in what he says, and the question is worth following up, for the sake of the light it throws on modern knowledge.  Just why do we believe that the earth is round?  I am not speaking of the few thousand astronomers, geographers and so forth who could give ocular proof, or have a theoretical knowledge of the proof, but of the ordinary newspaper-reading citizen, such as you or me.

    As for the Flat Earth theory, I believe I could refute it.  If you stand by the seashore on a clear day, you can see the masts and funnels of invisible ships passing along the horizons.  This phenomenon can only be explained by assuming that the earth’s surface is curved.  But it does not follow that the earth is spherical.  Imagine another theory called the Oval Earth theory, which claims that the earth is shaped like an egg.  What can I say against it?

    Against the Oval Earth man, the first card I can play is the analogy of the sun and moon.  The Oval Earth man promptly answers that I don’t know, by my own observation, that those bodies are spherical.  I only know that they are round, and they may perfectly well be flat discs.  I have no answer to that one.  Besides, he goes on, what reason have I for thinking that the earth must be the same shape as the sun and moon?  I can’t answer that one either.

    My second card is the earth’s shadow: when cast on the moon during eclipses, it appears to be the shadow of a round object.  But how do I know, demands the Oval Earth man, that eclipses of the moon are caused by the shadow of the earth?  The answer is that I don’t know, but have taken this piece of information blindly from newspaper articles and science booklets.

    Defeated in the minor exchanges, I now play my queen of trumps: the opinion of the experts.  The Astronomer Royal, who ought to know, tells me that the earth is round.  The Oval Earth man covers the queen with his king.  Have I tested the Astronomer Royal’s statement, and would I even know a way of testing it?  Here I bring out my ace.  Yes, I do know one test.  The astronomers can foretell eclipses, and this suggests that their opinions about the solar system are pretty sound.  I am therefore justified in accepting their say-so about the shape of the earth.

    If the Oval Earth man answers—what I believe is true—that the ancient Egyptians, who thought the sun goes round the earth, could also predict eclipses, then bang goes my ace.  I have only one card left: navigation.  People can sail ships round the world, and reach the places they aim at, by calculations which assume that the earth is spherical.  I believe that finishes the Oval Earth man, though even then he may possibly have some kind of counter.

    It will be seen that my reasons for thinking that the earth is round are rather precarious ones.  Yet this is an exceptionally elementary piece of information.  On most other questions I should have to fall back on the expert much earlier, and would be less able to test his pronouncements.  And much the greater part of our knowledge is at this level.  It does not rest on reasoning or on experiment, but on authority.  And how can it be otherwise, when the range of knowledge is so vast that the expert himself is an ignoramous as soon as he strays away from his own speciality?  Most people, if asked to prove that the earth is round, would not even bother to produce the rather weak arguments I have outlined above.  They would start off by saying that ‘everyone knows’ the earth to be round, and if pressed further, would become angry.  In a way Shaw is right.  This is a credulous age, and the burden of knowledge which we now have to carry is partly responsible.

    I added the emphasis on the line mentioning navigation. 

    Frank Reed

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