of the relative sizes of the Sun, Moon and the Earth
So stupendous is the work of the Greeks in art, literature, and philosophy that there is a tendency, even among those devoted to the study of the Greek spirit, to overlook or take for granted their achievements in other fields, e.g., medicine, geography, or mathematics."Fridays with Carl Kaeppel" continues with the next chapter in Off the Beaten Track in the Classics, focusing on mathematics in general and Aristarchus of Samos in particular. I’ll plead guilty to Kaeppel’s charge of overlooking or taking for granted achievements in other fields in classical Greece, even though I know many of them. In place of a bibliography of Greek mathematics, which he says would run many pages, Kaeppel recommends Sir Thomas Heath’s History of Greek Mathematics (as well as Heath’s “translation of The Thirteen Books of Euclid’s Elements, with introduction, notes and appendices; his Works of Archimedes, and last but not least, his definitive edition of Aristarchus.”) There are other works by Euclid, Archimedes, and Apollonius in the Teubner Series by Heiberg he recommends, too. Keep in mind Kaeppel was writing in the mid-1930s.
That is my excuse for commenting in this brief study on Greek mathematics in general and for providing a short account of a great and original genius, Aristarchus of Samos, who put forward the heliocentric hypothesis nearly two thousand years before Copernicus.
To disregard the Greek interest and achievement in natural science and mathematics is, in fact, to miss the cardinal characteristic of the Greek genius—its many-sidedness.
Some quotes and summaries from Kaeppel’s essay:
- "Mathematics, we have said emphatically, are a Greek creation, and a brief digression on this point is, perhaps, permissible. It has been said, and even written, by people who should know better, that the Greeks learned much of thei science and mathematics from Egypt. … In some of the papyri they [Egyptians] go farther; real mathematical problems are set and solved but, ‘with that curious incapacity for abstract thought’ which both Sayce and Erman stress, the Egyptians never formulated any real mathematical theorem. In short, like so much else, nay, like everything else in Egypt, mathematics had stopped and been perpetuated in the archaic stage. For in Egypt we have a civilization which is great in the sense of being enduring and firmly established, but not great in the sense of being far advanced intellectually and spiritually. It was a civilization, as the late March Phillips so well pointed out, not really based upon or nourished by the intellectual faculty, but supported by the strength of routine and usage, and it remained immovable, fixed in that archaic phase which precedes intellectual development.” (I have mentioned several times already that Kaeppel doesn’t pull his punches.)
- Kaeppel traces the development of Greek mathematics, a great mass of it accomplished in a short time period, especially the fifth and fourth centuries B.C. The third century sees Achimedes, “who may be said to have anticipated the integral calculus” and provided seminal work in hydrostatics. Apollonius of Perga completes his theory of geometrical conics around 200 B.C., completing the main body of Greek mathematics in four centuries.
- Astronomy was seen as a branch of mathematics. Many of the works of, say, Heraclides of Pontus has been lost but have been imitated and incorporated by later writers so that the earlier works can be reconstructed. Heraclides “put forward in detail the theory of the daily rotation of the earth about its own axis, and that the inferior planets, Mercury and Venus, revolve about the sun” (fourth century B.C.) but he stopped short of declaring a heliocentric model.
- Aristarchus’ life has been approximated as 310 to 230 B.C. Only one work has survived (On the Size and Distances of the Sun and the Moon, which does not claim the sun at the center of the galaxy), “but we know that he also wrote on light, vision and colours, and invented an improved sun-dial, the σκάφη, with a concave hemispherical surface instead of a plane. The treatise Size and Distances is based on Euclid but assumes things “that go beyond Euclid.” Ancient references make clear that Aristarchus put forward the heliocentric model after Size and Distances by such authors as Archimedes in “Sand-Reckoner” and Plutarch in his essay “On the Face of the Moon” (among others):
Cleanthes held that it was the duty of the Greeks to indict Aristarchus on the charge of impiety for putting in motion the Hearth of the Universe—supposing the heaven to remain at rest and the earth to revolve in an obique circle while it rotates at the same time about its own axis.
- Kaeppel again stresses how long it took before further strides were made in the sciences, especially mathematics, and how fragile the civilization that had been achieved could have been lost (a familiar theme if you have read the earlier posts on this book). As it was, almost two millennia elapsed before achievements rivaling the ancient Greeks occurred. Kaeppel also references a familiar zeitgeist I keep seeing from writers just before the start of World War II:
It [civilization] could have been, and can be, utterly destroyed, and the spectre of annihilation is, at this moment, hovering over it. Nothing is more futile or more dangerous than the facile optimism that regards progress as inevitable. Before our own, there have been some eleven or twelve civilizations of varying values; some of them we know only by their ruins.
I wish Kaeppel had followed up on the charge by Cleanthes. From this essay by Immanuel Velikovsky I found out that Cleanthes’ charge was in a tract titled “Against Aristarchus” and that it was about 150 years before we see followers adopting Aristarchus’ theories. Velikovsky also points out that Hipparchus, a well regarded contemporary of Aristarchus, rejected Aristarchus’ conclusions on a heliocentric model based on scientific grounds, not religious ones (like Cleanthes’ charges). If anything, these additional points help reinforce Kaeppel’s point on how fragile civilization and its advancements can be. Not to mention how charges of impiety weren't limited to philosophy and that junk science has been with us for a long time.
Aristarchus info at Wikipedia
The link to Immanuel Velikovsky's essay (again)
Another Aristarchus biography, this one at University of St Andrews, Scotland's School of Mathematics and Statistics