The Fall of Aristotle and The Rise of the Minervaeum II
Vitruvius and the Universal Theory of Gravity
“I do not know what I may appear to the world, but to myself I still seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
Vitruvius laughed, certainly not what his audience expected.
“But why do I chose the image of the beach? Three reasons, three people or more precisely three works we will discuss, before you honored guests all relating to the sea. Last one my newest and most likely final works!”
Unintentionally but certainly to impressive dramatic effect, he began to cough heavily. His time on this curious earth really was limited after all. And just when he began to understand it. Well, nothing he could do about that, he should know better to strain his health by acting overly theatrical. After all, if his latest work didn't impress, no rethoric trick would ever come close.
“First we need to recall Archimedes of Syracus’s work on the size of the universe.”
The Sand Reckoner of Archimedes
"There are some, King Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and the hollows of the earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken. But I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe.
Now you are aware that 'universe' is the name given by most astronomers to the sphere whose centre is the centre of the earth and whose radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account , as you have heard from astronomers. But Aristarchus of Samos brought out a book consisting of some hypotheses, in which the premisses lead to the result that the universe is many times greater than that now so called. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.
Now it is easy to see that this is impossible; for, since the centre of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere. We must however take Aristarchus to mean this: since we conceive the earth to be, as it were, the centre of the universe, the ratio which the earth bears to what we describe as the 'universe' is the same as the ratio which the sphere containing the circle in which he supposes the earth to revolve bears to the sphere of the fixed stars. For he adapts the proofs of his results to a hypothesis of this kind, and in particular he appears to suppose the magnitude of the sphere in which he represents the earth as moving to be equal to what we call the 'universe. I say then that, even if a sphere were made up of the sand, as great as Aristarchus supposes the sphere of the fixed stars to be, I shall still prove that, of the numbers named in the
Principles, some exceed in multitude the number of the sand which is equal in magnitude to the sphere referred to, provided that the following assumptions be made…”
Vitruvius Interlude
“When I was younger, I was mostly interested in his practical work on siege engines, but now that I have fought my battles for Roman glory, build our machines of conquest, the time came for me to expand into new frontiers, to conquer the world with my mind. And as our empire expands so should our knowledge. A friend who shares this attitude is Strabo of Pontus. We discussed some interesting observations of the nature of the tides.”
Statue of Strabo in his hometown Amaseia
Strabo and the Early History of Tides
Strabo was a Greek geographer, philosopher, and historian who lived in Asia Minor during the transitional period of the Roman Republic into the Roman Empire. Strabo was born to an affluent family from Amaseia in Pontus a city that he said was situated the approximate equivalent of 75 km from the Black Sea. Pontus had recently fallen to the Roman Republic, and although politically he was a proponent of Roman imperialism, Strabo belonged on his mother's side to a prominent family whose members had held important positions under the resisting regime of King Mithridates VI of Pontus.
Strabo's life was characterized by extensive travels. He journeyed to Egypt and Kush, as far west as coastal Tuscany and as far south as Ethiopia in addition to his travels in Asia Minor and the time he spent in Rome. Travel throughout the Mediterranean and Near East, especially for scholarly purposes, was popular during this era and was facilitated by the relative peace enjoyed throughout the reign of Augustus.
Strabo is most notable for his work "Geographika") which presented a descriptive history of people and places from different regions of the world known to his era. Although Strabo cited the antique Greek astronomers Eratosthenes and Hipparchus, acknowledging their astronomical and mathematical efforts towards geography, he claimed that a descriptive approach was more practical, such that his works were designed for statesmen who were more anthropologically than numerically concerned with the character of countries and regions. Still, he never stop being fascinated by the tides.
About 330 B.C. the Greek astronomer and explorer Pytheas made a long voyage, sailing from the western part of the Mediterranean Sea (where he lived in a Greek colony) to the British Isles. Observing the great ocean tides there, he made a fundamental discovery: The tides were in some way controlled by the Moon. This discovery can be considered the starting point of tidal research; it was published in Pytheas' "On the Ocean", now lost but quoted by other antique authors. Pytheas discovered not only that there were two high tides per lunar day, but also that the amplitude depended on the phases of the Moon.
The Greek scientists could not observe the tides at home because of their insignificance there. Nevertheless, around 150 BCE, the astronomer Seleucus of Seleucia found out that the two tides per day had unequal amplitudes when the Moon was far from the equator; this is what we today call the diurnal inequality. Seleucus was able to detect this phenomenon because his observations were made at the Red Sea, this being, according to modern tidal analyses, one of the few ocean areas where the diurnal inequality is relatively pronounced. The Greek scientist Poseidonios devoted a part of one of his written works to a review of the tidal knowledge of his time, including some of his own studies made at the Atlantic coast of Hispania around 100 BCE.
Strabon in his impressive book "Geographika" collected all these Idea and occasionally added upon them. He wrote for example: “When the moon rises above the horizon to the extent of a zodiacal sign [30°], the sea begins to swell, and perceptibly invades the land until the moon is in the meridian; but when the heavenly body has begun to decline, the sea retreats again, little by little; then invades the land again until the moon reaches the meridian below the earth; then retreats until the moon, moving round towards her risings, is a sign distant from the horizon. The flux and reflux become greatest about the time of the conjunction [new moon], and then diminish until the half-moon; and, again, they increase until the full moon and diminish again until the waning half-moon. If the moon is in the equinoctial signs [zero declination], the behavior of the tides is regular, but, in the solstitial signs [maximum declination], irregular, in respect both to amount and to speed, while, in each of the other signs, the relation is in proportion to the nearness of the moon's approach.”
He added that: “There is a spring at the [temple of] Heracleium at Gades, with a descent of only a few steps to the water (which is good to drink), and the spring behaves inversely to the flux and reflux of the sea, since it fails at the time of the flood-tides and fills up at the time of the ebb-tides”
This passage on reversed tides in a well is a remarkable one since it represents, in fact, the first observations of earth tides in the form of tidal strain. Although the phenomenon in the well had been known for a long time it appears that Poseidonios was the first scientist to study it, during his above-mentioned scientific travel to Hispania. Poseidonios, while admitting that "the ebb-tide often occurs at the particular time of the well's fullness", did not believe that it really had anything to do with the tides. Strabon, however, discussing the problem in detail, arrives at the conclusion that the phenomenon somehow must be a tidal one.
Vitruvius Interlude
“Now this question the question remains, how does the moon influence the sea or for that matter the fiendishly contrarian little well in Hispania? The answer of course is gravitational attraction, a subject that I have explored quite a bit.”
Despite his outward humbleness he obviously knew that he was one of the greatest contributor to the understanding of gravity in the known world. What kept him grounded however were precisely the little mysterious like the well of Gades, who’s behavior still didn’t fit in his new framework.
Notes and Sources
As you might have guessed from the borrowed quote in the beginning in this timeline Vitruvius is going to be their version of Galileo as well as Newton, although with a bit less math and a lot more tinkering.
As mentioned earlier he also was fascinated with the phenomenon of tides.A Concise History of the Theoreis of Tides Precession-Nutation and Polar Motion(From Antiquity to 1950) by Martin Ekman
The Sand Reckoner of Archimedes translated by Thomas L. Heath (Original publication: Cambridge University Press, 1897).
wikipedia: Strabo etc.
People
Marcus Vitruvius Pollio (79 BCE, c. 11 BCE) - In this timeline
Strabo (64 or 63 BCE – c. 24 ACE)
