Saturday, July 02, 2016

Flat-earth cartography

I don't think it's worthwhile to debate flat-earthers. And I didn't initiate this debate. But one thing leads to another, so I will say a bit more. There are folks more qualified than I to discuss this. Since, however, I doubt there are any scientifically qualified flat-earthers, my only disadvantage is that if you spend all your leisure time defending a conspiracy theory, you have prepared answers to stock objections. Likewise, you can cite factoids that ordinary folks haven't investigated. 

1. I Googled some modern flat-earth maps. One thing I notice is that there doesn't seem to be any standardization in flat-earth circles regarding the distribution of oceans and contingents. Flat-earth maps vary. 

That, itself, is problematic for zetetic astronomy. If you can't show us, in detail, what the flat earth looks like, what's your empirical evidence that the earth is, indeed, flat?

2. That said, the maps had something in common. They resemble a projection map of the globe. Reducing a global image to a flat map.

The difference is that flat-earth maps take a topdown approach whereas conventional maps take a sideways view. The flat-earth maps I saw have the north pole at the center, surrounded by the continents. Continents in the northern hemisphere are closer to the center, while continents in the southern hemisphere are closer to the circumference. Flat-earth maps vary somewhat on where to put the oceans. 

3. However, this immediately poses problems for flat-earthers:

i) Since, on their view, the sun shines directly on what would be the northern hemisphere, how does that square with climate zones? 

ii) Likewise, how does that square with time zones? Suppose a flat-earther views the sun like a spotlight that moves incrementally across the terrestrial disk. Even if that would explain longitudinal alternations in day and night, how would that synchronize with latitudinal alternations? Everything above and below the spotlight would be dark. 

iii) Even more problematic, once the sun completes its progression from left to right, it would have to travel under the flat earth to resume the cycle. But that would plunge the entire earth into darkness for however long it takes the sun to pass under the flat earth. 

4. It's demonstrably the case that a pilot can, by flying continuously in a straight line, return to his point of departure. How is that possible on a flat earth? 

Sure, if you fly in a circle on a disk, you can return to your point of departure. But I'm talking about a flight path in a straight line.

It is, of course, possible for a trajectory to be both straight and circular. But that only works on a sphere where you have an extra coordinate. 

5. I should have been more explicit about what I mean regarding satellite photography. 

i) I'm not primarily alluding to the fact that the earth appears to be spherical according to satellite photography. Rather, this is what I mean. Consider a class room globe. You can only see whatever part of the earth is facing the viewer. To see the whole earth, you must either walk around the globe or remain in place and spin the globe. 

ii) We have an equivalent situation with spy satellites and earth observation satellites. They can't photograph the earth all at once. They only display a portion of the earth facing the satellite. 

But as the earth rotates under the satellite, in the course of one rotation period the satellite can photograph the entire earth. That makes perfect sense if the earth is spherical and spinning on its axis. 

iii) If, by contrast, the earth is flat, why can't we see the whole earth from space, all at once, just like we can see a flat map of the earth at a glance?

iv) And even if a flat-earther postulates that a satellite is too close for a wide shot, there's still another problem. Suppose a satellite begins to photograph the earth at the meridian. After an orbital period, the meridian is once again facing the satellite. Continuous photography tracks the continuous counterclockwise rotation of the earth.

If, however, the earth is flat, and the satellite is photographing the earth from left to right or right to left, then it must reverse direction to return to the starting-point. Yet, when photographing the earth from space, there is no break. You see the same portions of the earth coming into view in the same direction. Admittedly, I'm no expert on satellite photography, but do flat-earthers have any hard evidence to the contrary?

6. In addition, zetetic astronomy must rewrite the laws of physics. That's extremely complicated. Has any flat-earther produced detailed alternative physics to make it work? Is there anything comparable to the level of detail and empirical confirmation in standard astrophysics? 

7. Finally, flat-earthers have to prop up their theory by invoking conspiracy theories to discount empirical evidence that runs counter to zetetic astronomy. Now, I don't deny the existence of conspiracies. However, a conspiracy theory loses credibility when the scale of the conspiracy involves too many independent players, sometimes with rival motivations. As well as too many people who must somehow be kept in the dark. 


  1. I'm not a flat-earther, but are you sure you're not arguing a straw man here?

    For instance, the flat earth explanations I'm aware don't have the sun moving across the flat earth, but rather orbiting above the disc of the earth. The sun is much smaller and much closer than we imagine, so that when the sun moves far away, it looks as if it's disappearing, and its light fades.

    1. I don't see the difference between moving across the flat earth and orbiting above the disc of the earth. In both cases it moves over a flat (disk) earth.

      I also don't see how making it smaller and closer affects my arguments. You need to spell that out.

    2. To flesh things out, on a flat-earth view, either the area of sunlight cast on the terrestrial disk is bigger than the disk or smaller than the disk. If bigger, then there's a period when the sun would illuminate the entire side of the terrestrial disk. But that's inconsistent with time zones.

      Conversely, if smaller, then while transit of the sun might account for a horizontal alternation of light and dark, the vertical portion not covered by sunlight would be perpetually night.

      Moreover, whether bigger or smaller, once the sun completes its orbit from one side to the other across the face of the terrestrial disk, it must then go around the back of the disk, moving in the same direction, to resume the cycle. But during that period, the whole would be pitch black–which never happens in reality.

    3. Sun orbiting above flat disc poses another problem. Sun is always in zenith somewhere. Has anyone ever obeserved sun in zenith every day throughout the year?

  2. In addition:

    1. If the Earth is flat, not only would we have to change the laws of physics, but other scientific laws as well. Take photosynthesis. If the Earth is regularly plunged into darkness for x number of hours, then how would this affect plants which require photosynthesis to properly function, etc.?

    2. I recently saw this:

    "I made this model to explain the basic idea about the flat earth model. This animation is not accurate, the sun and moon orbits change during the year."

    The animator admits the animation isn't meant to be "accurate" but simply "to explain the basic idea". This is hardly the first time I've read something like this from flat earthers. That's one of their big problems: they think it's fine to be vague and non-specific when the specifics are often what make the difference between true vs. fanciful ideas.

  3. Sorry, Steve, but your arguments against a flat earth don’t work.

    A flat earth model of the universe can easily be made empirically equivalent to a spherical earth model. Simply apply a mathematical transformation called a "geometric inversion". For each point in the universe, measure its distance R from, say, the earth’s South Pole, and move this point along the Pole-to-point half-line to a new distance 1/R.

    This transforms the spherical surface of the earth to a flat disk, centered on the North Pole, with the South Pole infinitely far away (i.e., this is the stereographic projection of geography). All points inside the Earth are transferred beneath the disk; all points in the sky are transferred above the disk. Galaxies that were infinitely far away end up a short distance above the new North Pole.

    The laws of physics are also transformed, with consequences that may seem strange for those accustomed to thinking in terms of the more conventional universe. For example, sunlight now travels in circular arcs, the sun and stars become much smaller than the (now infinite) earth, etc. See my post
    Mathematical models and reality:

    Terrestrial objects increase in size as they travel away from the North Pole, becoming infinitely large at the South Pole. However, since inversion is a conformal transformation, local shapes are preserved. Hence you won’t notice any changes as you travel.

    It is not my intent to defend a flat earth, but only to point out that, with some ingenuity, one can construct a mathematical model of the universe with almost any feature one wishes (the Duhem-Quine thesis), as long as one is willing to make adjustments elsewhere (e.g., sunrays become circular arcs, size is not preserved, etc.).

    Since this flat-earth model is empirically equivalent to the spherical earth model, the choice between these models must be made on the basis of non-empirical factors, such as philosophical or theological considerations.

    1. From a purely mathematical standpoint, Dr. Byl is correct. One can mathematically model the surface of the earth as a sphere or as an infinite plane, and it's trivial to transform one model into another. But then, doesn't that just trivialize the whole debate?

      I have no experience of debating modern flat-earthers (thankfully) but I suspect they believe the debate is over more than the empirical adequacy of competing mathematical models. Rather, they think that from a suitably distant vantage point, the earth would actually look flat to us, not spherical, and that our perceptions would be veridical. If they don't think that, then I honestly don't understand why the debate holds any interest.

      It looks to me as though Dr. Byl is approaching the debate as a scientific anti-realist (perhaps some kind of instrumentalist). His appeal to Duhem-Quine certainly suggests that. But are most flat-earth defenders today anti-realists? I doubt it.

      If it were just a matter of empirically equivalent mathematical models, there would be no need for conspiratorial theories to "explain away" the supposed empirical evidence for a spherical earth.

    2. Additionally, it doesn't account for the mass of the earth in the application of the gravitational constant, so it doesn't account for all the understood laws of physics.

      Anyway, the application of a transformation to flatten out the earth is counterintuitive when the observation of a flat earth to begin with is observationally intuitive (if fraught with a denial of aided observation). It's what we might call grasping at straws: the development of an exceptionally complex explanation to justify an underinformed belief.

  4. There's a difference between an abstract actual infinite and a concrete actual infinite. When you mention infinity in relation to geometric inversion, I assume you're discussing mathematical relations as abstract objects. If so, it doesn't follow that physical instances of mathematical abstractions can exemplify the outer limits of mathematical abstractions (e.g. infinitely large, infinitely small). What's possible for spaceless, timeless relations may not be possible for spatiotemporal relations, if matter is granular. Kinda like the Planck length.

    This goes back to ancient debates over the infinite divisibility of time and space. So it's unclear to me that a purely mathematical model will coincide with the physical universe. At best, we may expect it a physical approximation.

    For instance, how can physical objects be infinitely large? Is there not an upper limit to convalent bonding?

    You may say that's why there must be corresponding adjustments in the laws of physics, but is that anything other than a verbal placeholder with little conceptual content?

    1. Dr. Byl's argument reminds me of science fiction stories about miniaturizing humans. No doubt it's possible to produce a mathematically coherent model of a human being who's several orders of magnitude larger or smaller. You can scale it up or down, but preserve the same internal relations.

      Yet it's not physically possible for a viable human being to be several orders of magnitude larger or smaller. A human being can't be as tall as a skyscraper or as small as a molecule. Anything material has in-built physical constraints. (Not that humans are purely physical.)

      In fairness, he admits that a flat-earth cosmology requires different laws. But I think that's a token concession. Has any flat-earther ever developed a detailed system of alternative physics to make that work? If not, then flat-earth cosmology isn't competitive with the standard view.

      I don't think it's metaphysically possible for physical space to instantiate actual infinities, whether infinitely large or infinitely small (or wide or deep or long or thin).

      So I guess one question concerns Byl's ontology of math–what he thinks mathematical objects are, and how they interface with the physical world.

      To me, his position is like confusing what's possible in a dream with what's possible in reality. Surreal things can happen in dreams because dreams are imaginary. Dreamscapes aren't subject to physical constraints. Dreams are visualized ideas.

      But I think energy and matter are intrinsically finite states. It may be a convenient simplification or idealization in physics to speak of infinities or infinitesimals, but I don't take that literally.

    2. It's like all of those physics problems..."Assume a perfectly flat and frictionless surface..."

      Sure, it's mathematically possible, and sometimes helpful, to see things that way, but I always wanted to answer those questions with:

      "If you can assume a perfectly flat and frictionless surface, I can assume the answer is 14.3 ..."