Goldfish and Hollow Earth

It is perhaps a little odd that Stephen Hawking & Leonard Mlodinow’s popular science book The Grand Design devotes a whole chapter to the philosophical question “What is reality?”. It opens with an amusing anecdote about an Italian law which apparently considers keeping goldfish in curved bowls a form of animal cruelty, because, forced to observe the world from inside a curved surface, the fish would develop a distorted view of reality. Hawking explains that it is possible for the lost souls living in fishbowls to develop a version of physics based on non-euclidean geometry, and it would be as real as ours. This point of view, which Hawking & Mlodinow call model-dependant realism, has inspired some lively debates (and I agree with critics that the authors failed to give a coherent statement of the idea) but at least in the context of fishbowl-based physics, I believe it is hardly controversial. Laws in physics can be formulated in many different ways – most of us who took a class or two in physics take it for granted that the various formulations of classical mechanics (not to mention quantum mechanics) are equivalent to each other. Professors typically switch from one to another without even bothering to make a comment on the philosophical implications.

The discussion becomes a little more uncomfortable in the next page, where the authors review the development of celestial mechanics:

So which is real, the Ptolemaic or Copernican system? Although it is not uncommon for people to say that Copernicus proved Ptolemy wrong, that is not true. As in the case of our normal view versus that of the goldfish, one can use either picture as a model of the universe, for our observations of the heavens can be explained by assuming either the earth or the sun to be at rest. Despite its role in philosophical debates over the nature of our universe, the real advantage of the Copernican system is simply that the equations of motion are much simpler in the frame of reference in which the sun is at rest.

Not being a philosophically minded person, I am not going to offer any deep thoughts about it, except noting that, taken to the extreme, this line of reasoning can lead to some amusing, if slightly strange, conclusions. One astonishing example is given in Chapter 2 of Martin Gardener’s book On the Wild Side (1992). As it turns out, the hollow earth theory, which postulates that the entire universe resides in the closed space surrounded by the shell of earth and that we live on the concave side of the shell, is not merely the stuff of mythology and conspiracy theories [1]. The idea can in fact be formulated into a coherent theory of physics. Mostafa Abdelkader [2], an egyptian mathematician, applied a geometrical transformation, which maps every point outside a sphere to a point inside the sphere, to known physics laws and derived a new set of laws which cannot be distinguished from the canonical laws by any empirical observations. The hollow earth model of the universe is in fact as real as the familiar textbook model! That sounds bizarre. How can that possibly be true? Wouldn’t that contradict some observations? Isn’t the space surrounded by the shell of earth too small to contain the entire universe? Ah, you see, the new laws say that objects become smaller and smaller and travel slower and slower as they approach the center of earth. To an astronaut trekking towards the center, the universe therefore appears to be vast and boundless. But stars far away from us would have to be too tiny to be observed by telescopes, wouldn’t they? The inversion takes care of that too. The new laws dictate that light travels in complicated curved paths and changes its speed, just so that stars look exactly the same as what we observe. Remember, hollow earth is reality, at least according to model-dependent realism.

But is it? Gardener argues that we should reject hollow earth physics, not for empiricism, but for the principle of parsimony. Consider this: you can perform the inversion not with respect to earth, but with respect to any planet or star. You’ll derive different models of the universe. They will all be real under model-dependent realism, but the choice of the point of inversion is unnecessary, arbitrary, and it comes with the price of vastly more complicated mathematics. To me, it makes sense to state that our conventional model of the universe is a better model than the hollow earth model, because it removes that arbitrariness. But is it more real? That is a difficult question but perhaps we can say that it is less distorted.

If I were an iPad developer I’d spend a few months developing a simulator of the hollow earth model of the universe. Wouldn’t it be great if you could see how planets (or galaxies) travel in this view of reality?

Note 1: Hitler allegedly was fascinated by the hollow earth theory. Nazi scientists supposedly launched a few ballistic missiles whose design was based on the assumption of a concave earth. Keep in mind that I learned everything about world history from Umberto Eco’s Foucault’s Pendulum.

Note 2: Interestingly enough, the work of Mostafa Abdelkader was published in an Australian journal called Speculations in Science and Technology (vol 6, 1983, 81-89). According to Gardner, this journal is devoted to “unorthodox science” with Paul Feyerabend on the editorial board.


~ by hhyu on April 4, 2011.

2 Responses to “Goldfish and Hollow Earth”

  1. the Note about Hitler believing in the Hollow earth does not refer to the eye-fish projection like model
    but is about the belief that earth is spherical but the poles are holes that lead to and inside surface world that contain a inside earth sun (shambala)
    the ballistics that you mentioned made me understand why an author
    used an artillery piece pointing to the zenith in a O’Neill cylinder in fictionalized operation Valkyrie in space

  2. I think I made it very clear that the “hollow earth” physics I described is very different from Agartha and related legends. That’s why it was mentioned in a note.

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