Published in Memorie della Società Astronomica Italiana, Special Number1, Vol. 3, pp. 257-262 (2002).

FLAT WORLDS:TODAY AND IN ANTIQUITY

DIDIER DE FONTAINE

University of California, Berkeley, CA, 94720 USA

ABSTRACT

So, Euclid was right after all! Very recent results from two largely independent astrophysics groups have shown the geometry of the Universe to be practically "flat", meaning that the radius of curvature of space as a whole is extremely large with respect to the radius of the observable Universe. It is interesting to compare this finding with the pre-Hellenistic belief that the world was flat, at least on the scale of the observable universe of the times. In such early days, the religious implications of the flat geometry were straightforward: the assumed three-tiered universe, Hell - Earth - Heaven, defined a unique "morality vector" pointing straight up. Later Greco-Roman introduction of curvature, with the attendant loss of a unique direction, must have played philosophical and religious havoc on the culture of the times. It remains to be seen whether the new concepts of accelerated universal expansion, flatness, dark matter, "quintessence", will be as disturbing to present culture and religion as were previous scientific revolutions.

 

As inhabitants of the cosmos, the way we conduct our lives has been deeply influenced by the world around us, and our thoughts and beliefs by our perception of the Cosmos, a world view which has changed dramatically in the course of time, and continues to evolve at an ever-accelerating pace. Today, we can chart the evolution of cosmology, the technical term for world perception, by examining the historical record of ancient myths and religions as narrated in philosophical and theological writings and illustrated by works of art; i.e. by looking at the influence of astronomy on art, precisely the topic of this Conference.

These last few years, extraordinary developments have occurred in our conception of what the universe may be like, and many unanswered questions have been raised. It may therefore be of some use to inquire how the evolution of cosmological concepts influenced everyday life and art in the past. "In the beginning", to borrow from Genesis, the earth must have appeared generally flat to early man, perhaps a disk a few hundred kilometers in diameter. Life on our home disk must have seemed bewildering, chaotic, painful, unpredictable.

Figure 1. Early flat-earth cosmology with starry dome above and the underworld below, featuring the vector of good and evil

The only portion of the cosmos which made sense, because regular and predictable, was that of heaven with its well-behaved movement of planets and stars (though the distinction between the two did not exist at the time). Surely only gods could ordain such a structured universe. It followed that the only way for us lowly terrestrial creatures to cope with life and its random complexities was to read the mind of the gods (or God), to propitiate the divinities by offerings, sacrifices, prayers, rituals. Therefore the heavens (or Heaven) must be the locus of all that is good in the world, while the earth is but the locus of what is mediocre, neither very good nor very bad. What about the subterranean locus beneath our feet? Surely, that is not a nice place: it is the realm of the dead -- since we bury our dead -- and also the realm of hellish fire which appears to us occasionally in the form of red-hot lava flows which destroys crops, habitats, people, everything that lies in their path. Hence, the underworld is the realm of evil, one that can only be mentioned by God-fearing people in hushed tones, if at all. To this simplistic view corresponds an equally simple cosmology, depicted schematically in Figure 1. This vertical section of the ancient universe features the one-dimensional stratification: Hell —Earth —Heaven, with its fixed progression from bad, to mediocre, to good. I have therefore indicated that progression by a vector, the vector of good and evil. How convenient: early cosmology has morality built into it; there was perfect agreement between science and theology, between astronomy and astrology. How long did this happy state of affairs last? The answer of course depends on which culture one is referring to, and in a given culture, what stratum of the population. In Mesopotamia, early Egypt, Biblical Israel, early Greece, the flat-earth model was unchallenged, as described for example in J. E. Wright's interesting monograph "the Early History of Heaven" (2000). In classical Greece, the presocratic philosophers, such as Leucippus
(ca. 440 BCE) and Democritus (ca. 460-370 BCE) apparently believed in a flat earth, at least according to Aristotle, for we have few extant writings by the presocratics concerning their favored cosmological models. Aristotle himself (324-322 BCE) and also Plato (427-347 BCE) however, had reasons to maintain that the earth had to be spherical. Somewhat later, Eratosthenes (ca. 275-195 BCE) actually measured the radius of the earth, leaving no doubt, at least in the educated public, as to the earth's overall sphericity. How much of this knowledge trickled down to ordinary people is hard to ascertain.

Figure 2. "The third day of creation", outside panel of Bosch's Garden of Earthly delights

 

 

As children, we were told that "Columbus proved that the earth was round". But surely he was not the first, as we have just seen. Indeed, in a recent book, Danielson (2000) writes "a strangely persistent myth is that before 1492, people thought the earth was flat. On the contrary, the ancient Greeks and others knew that the earth was spherical". That is true, but matters are not so straightforward. In an interesting monograph entitled De la terre plate au globe terrestre, Randles (1980) argues that before about 1480 the medieval world struggled with attempts to reconcile the flat-earth approach of Biblical dogma and the Aristotelian view of sphericity. It was apparent that Aristotle's overall model of concentric spheres of the four elements: earth as the inner sphere, surrounded by spherical shells of water, then of air, then fire, was empirically incorrect, yet a spherical earth had some basis of fact and could not be discounted. In addition, Aristotle's renown was such as to make him virtually infallible. But the Catholic popes were infallible too, so that a flat earth with Jerusalem at the center of the disc was the only dogmatically acceptable solution to the cosmological problem. As a result, various hybrid descriptions were proposed, for example featuring a large watery sphere on which floated a small island of flat earth, the realm of humanity, or (Christian) oecumene.

Figure 3. Detail of upper corner of Figure 2, God the Father

There was also the pesky problem of the vector of good and evil: in a spherical earth, that vector points in all directions, like a compass that has lost its bearing. By abandoning the flat cosmology of Figure 1, humanity seemed to have lost its moral bearing as well! In addition, the center of the earth (Hell?) became the center of the universe, instead of Jerusalem, hardly a healthy development.

It is therefore not surprising that artists of the time of Columbus clung to flat-earth representations, as illustrated for example on the outside panels of Hieronymous Bosch's (ca. 1450-1516) famous triptych the "Garden of Earthly Delights". The painting on these panels, reproduced here in Figure 2, are said to depict the third day of creation, when God made the land appear and bear vegetation. As can be seen, the earth is decidedly flat, but placed inside a crystalline sphere (certain art critics notwithstanding, I maintain that the bright streaks are reflections on the crystalline sphere, not a rainbow). At the upper left-hand corner of the painting, a small circular smudge is seen which, when blown up, reveals God Himself (Figure 3). From this and many other examples, it is clear that artists of the time were still very uncomfortable with the idea of a spherical earth, some 1700 years after Eratosthenes had measured its radius! What should have become common knowledge after the time of Christ was suppressed, or at least hopelessly discombobulated by outmoded sacred doctrines. The reluctance of medieval theologians, from Saint Augustine onwards, to accept an inhabited world of spherical shape could be attributed to the apparent absurdity of humans walking upside down at the antipodes, to the apparent contradiction with scriptures, particularly the loss of Jerusalem as the center of the Universe, to the apparent parting of the ways between science and religion caused in part by the loss of a unique morality vector, not stated explicitly, but implied by canonical thinking of the times. Today, we find the Eratosthenes experiment quite convincing; not then: the Greek philosophers had reasoned as astronomers and mathematicians, providing arguments which carried little weight in the face of common sense bolstered by sacred texts. The conversion to spherical-earth acceptance took time: Randles (1980) subtitles his monograph "a rapid epistemological mutation [from flat to round], 1480-1520", i.e. from about 10 years before the start of Columbus's historic journeys to Magellan's death in the Philippines.

 

After the return to Spain of Magellan's Captain Elcano in 1522, all doubts about the sphericity of the earth vanished. Hence, our school teachers were at least partly correct: it was not the lofty reasoning of Greek philosophers which convinced anyone to give up their cherished flat cosmology, it was experiment pure and simple, in the form of the heroic explorations of Portuguese and Spanish navigators. But let us not belittle theory too much; it is doubtful that these hardy sailors would have ventured quite so confidently into the bleak unknown if their faith had not been supported by at least hints of spherical cosmology.

But hardly had the European intelligentsia accustomed itself to the new paradigm that another cosmological revolution burst upon the scene: the Copernican revolution (1543, year of publication of de Revolutionibus, also of the death of its author). Note that from about 1510 to 1514, a time span included between the Columbus and Magellan journeys, Copernicus circulated privately a short manuscript summarizing his heliocentric model: the Commentariolus. At first, reaction to the Copernican model seems to have been rather mild; it was only when Galileo (1564-1642), armed with a telescope instead of holy writ, championed heliocentrism that the Church reacted strongly. The story is too familiar for me to elaborate here; but the tale is well worth re-reading, for example in the popular account given by science writer Dava Sobel (1999). Suffice it to point out that, if the sphericity revolution had caused humanity to lose its biblical center, the heliocentric revolution caused it to lose its terrestrial center as well. Not only was Jerusalem not the center of the Universe, the earth itself was not. In the language I have been using here, the morality vector was not only spinning in every direction, it appeared to be centered on the sun, a pagan divinity at best! In the language of physics, the morality vector, once unique in direction and position, gained spherical symmetry, then translational symmetry as a result of two successive cosmological revolutions. Astronomy could no longer support religion, nor religion astronomy.

Graphic representations of ancestral cosmologies are reproduced in the beautiful book by Professor Francesco Bertola, Imago Mundi (1997), a copy of which was available for consultation by the participants at this Conference. See for example the miniature by Hildegard von Bingen (1098-1179) depicting a spherical earth, spouting huge trees, surrounded by water, surrounded by air, surrounded by fire in an extraordinary admixture of Aristotelian philosophy and early Christian mysticism. Later, the layering of Aristotelian elements were replaced by concentric circles representing the orbits of various planets, including the sun and moon, around the earth, throughout the XIVth, XVth and XVIIth centuries. Amid all of these florid representation, which usually owed more to art and astrology than to science, one illustration in Professor Bertola's book stands out in its stark simplicity: a set of concentric circles is shown labeled Sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, the fixed Stars, in proper order. This purely geometrical drawing is accompanied by no gods, angels, dragons, or Zodiac signs. The source? An autographed manuscript by Copernicus, dated 1520-1541. And yet, even in 1777, the two cosmological systems, Ptmolemaic and Copernican, were shown side by side in atlases such as the one by Antonio Zatta (Bertola 1997), as if to indicate that the matter of geo-centricity versus helio-centricity had not been settled yet in the XVIIIth century, just as in XXth century United States certain school boards wish to have Darwinism and "Creationism" taught side by side.

Today, with the discovery that the sun is but a star and stars are suns, often surrounded by planets, even our solar system is no longer at the center of the universe; the universe has no center at all! Does that not give us an uncomfortable sense of floating about aimlessly, purposelessly in an uncaring world which is mostly void? We have come frighteningly far from a friendly universe, built to order, centered upon ourselves, with everything that is good above us, and everything that is bad below, a blueprint for our moral aspirations. Even our Galaxy is but an island of stars floating in an immense ocean of nothingness, dotted here and there by other galaxies until the speed-of-light horizon is reached, some 15 billion light years away, marking the limit of the so-called visible universe. Does the universe extend beyond that horizon which is, by definition, centered on ourselves? It must, if only because of the new paradigm that we do not occupy a privileged place in the universe; but how far does it extend? The inflationary version of the Big Bang (BB) theory has provided a tentative answer (Guth 1997): because the universe went through a phase of exponentially accelerating expansion, before settling down to a more leisurely-paced one, the universe today

Figure 4. Geometrically flat space (disk) embedded in higher dimensions. Compare Figures 1 and 2.

must be immensely larger than the visible one. As explained by Guth, since contemporary measurements appeared to indicate that the universe was geometrically flat, i.e. that the sum of the interior angles of a triangle drawn in our space was equal to 180 degrees (Euclid was right!), it must have been so very shortly after the BB. Very recently (Jaffe at al. 2001) two research groups have indeed shown space to be "flat" (or nearly so) some 300,000 years after the BB, the blink of an eye on a cosmological time scale.

So flatness returns to cosmology, but in a very different mode than that of the ancients, of course. Somewhat in the manner of Figure 1, I have tried to convey the modern flat cosmology very schematically by imagining that space is two- rather than three-dimensional, as indicated in Figure 4. Facetiously, I have presented matters in the manner of Bosch, in his "Third Day of Creation" (see Figure 2). Not knowing how to represent God, I simply inscribed a question mark inside a circle in the upper left corner, off in higher-dimensional space. The disc representing our space in reduced dimensionality could be extended indefinitely. This new flat cosmology does not restore any up-down, good-bad hierarchy, however; it is gone forever.

In fact, gone forever is the old paradigm of our centrality, of our self-importance. We are no longer God's chosen people, living on God's chosen earth, in God's chosen solar system, inside God's chosen galaxy.

Oh Paradigm Lost!

The author gratefully acknowledges a travel grant from the Academic Senate of the University of California, Berkeley.

REFERENCES

Bertola, F. 1997, Imago Mundi, Biblos, Cittadella, Italy.
Danielson, D. R., 2000, The Book of the Cosmos, Helix Books, Cambridge, Mass.
Guth, A., 1997, The Inflationary Universe, Helix Books, Reading, Mass.
Jaffe, A. H. et al. 2001, Physical Review Letters 86, 3475.
Randles, W. G. L., 1980, de la terre plate au globe terrestre, Librairie Armand Colin, Paris.
Sobel, D., 1999, Galileo's Daughter, Walker Publishing Co., New York.
Wright, J. E., 2000, The Early History of Heaven, Oxford University Press, Oxford, New York.