How I extended Galileo’s work!

I have already mentioned it: it is about time that I present the topics that I am interested in my work. As I have indicated on this site home page and as can be deduced from my resume, my areas of expertise are applied mathematics and theoretical computer science. My scope is physical oceanography. Specifically, I am reproducing ocean dynamics on computers.

However, though being a still evolving discipline, the study of ocean dynamics has a long history. The oldest references I have found were written during the antique times. The main topic on ocean dynamics they address is tide. I intend to present this story here. Much of the information you will find in the following comes from Bernard Simon’s La Marée océanique côtière¹B. Simon, 2007. La Marée océanique côtière, collection “Synthèses”, Institut océanographique éditeur.. The following is an extract from the introduction of my Ph.D. thesis²Y. Le Bars, 2010. Modélisation de la dynamique océanique barotrope dans l’estuaire et le plateau amazoniens, Ph.D. thesis, Université de Toulouse III – Paul Sabatier.. This thesis focused on the development of an ocean model and its application to the estuary of the Amazon, so I do not claim to have achieved a definitive historical study: the following is a summary, albeit detailed, but with all the limitations of this exercise.

Early observations

Although Homer (late eighth century bc) made some allusion to tide, to my knowledge one of the first authors actually mentioning it which we have kept track is Herodotus (circa 484 or 482 bc – circa 425 bc). He tells about the rise and lowering of water daily from the Red Sea, without giving further details. In Plato's dialogue (428 or 427 bc – 347 or 346 bc) entitled Timaeus³Πλάτων, circa 360 bc. Τίμαιος. An English version can be found in: F. M. Cornford, 1997. Plato's Cosmology: the Timaeus of Plato, Translated with a Running Commentary, Hackett Publishing Company, Inc. It also can be read on line., tides are explained by the surge of ocean water masses induced from rivers flooding and streams. Heraclides Ponticus (388 bc – circa 310 bc), for his part, assumes that the Moon and the Sun are the sources of the tides. Meanwhile, an unknown author writing under the name of Aristotle in On the Universe⁴Ἀριστοτέλης, between 350 and 200 bc. Περὶ Κόσμου., noted that the tide follows the movement of the Moon.

However, I consider the study of ocean dynamics does not really start until about 330 bc. Pytheas then leaves the Greek colony Massilia, to later become Marseilles, for a long trip to the British Isles (he even likely reach the Arctic Circle). There, he saw tides of unsuspected amplitude in the Mediterranean world. Not only he noticed that there were two high and low tides by lunar day, but also that the tidal range depended on the phases of the Moon. Unfortunately, there are only a few elements of Pytheas travelogue. The book On the Ocean he wrote on his return having disappeared, only remaining analyses from historians and geographers of the time, such Polybius (between 210 and 202 bc – 126 bc) or Eratosthenes (circa 276 bc – circa 194 bc).

At about the same period, Selerrens of Babylon observed tides in the Persian Gulf and reported the effects of the declination⁵The declination is is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. on the tidal range. Some 150 years later, the Greek astronomer Selukos (between 358 and 354 bc – 281 bc), observing the tide of the Red Sea, discovered the diurnal inequality and connected their amplitude to the variations of the Moon declination.

Then, in the first century bc, Posidonius of Apameia (circa 135 bc – circa 51 bc) establishes for the coasts of Spain a table showing the concordance of diurnal, semi-diurnal and monthly tidal variations with the movements of the Moon and the Sun. Strabo (circa 57 bc – between 21 and 25 ad) at the beginning of the Christian era, describes the tides of Portugal, England, Denmark, Italy and the Persian Gulf⁶Στράϐων. Γεωγραφικά, 17 volumes.. He is the one who was the most interested in Pytheas travel. He is also his first detractor, concluding that he is a storyteller, in particular because he considered implausible that the sea could be frozen.

Around the same time, Pliny the Elder (23 ad – 79 ad), another Pytheas reader, in Natural History⁷Gaius Plinius Secundus, circa 77. Naturalis Historia, 37 volumes. An English version can be found in: J. F. Healy, 2004. Pliny the Elder: Natural History: A Selection, Penguin Classics. It also can be read on line., mentions the lunitidal interval⁸The lunitidal interval measures the time lag from the moon passing overhead, to the next high or low tide., the age of the tide – that is to say, the lag between high tide with the syzygy time (full moon or new moon) –, ‘earthly effects of celestial phenomena always being seen with some delay, such as thunder with lightning,’ and annual variations in the amplitude of high tides. According to him, the tide phenomenon is connected with the Sun and the Moon:

‘On the nature of water, finally, much has already been said, but the advance and retreat of the waves are the most extraordinary. Anyway this offers plenty of variety, its cause lies in the Sun and the Moon.’

He observes two tides per day:

‘When the Moon rises twice, the sea goes up and down twice in each 24-hour interval.’

Finally, he made the observation that the tide is not exactly semi-diurnal:

‘Tides never occur at the same time as the previous day, as if they were panting through the influence of a greedy star that attracts to itself the seas to drink.’

Thus, two millennia ago, the most important characteristics of tide were known, especially through observations of the Greeks in the British Isles and in the Red Sea. However, it was not something like 1700 years before a satisfactory explanation was given for this phenomenon. During this period, various authors have attempted to explain the tides, with more or less success.

Early theories

Augustine of Hippo (354 – 430), in his philosophical works, attempts an explanation of tides through an interpretation of Genesis. Meanwhile, the Venerable Bede (673 – 735), a British monk, thought that the ebb is due to the breath of the Moon on the water, the flow occurring when it goes away⁹Beda Venerabilis, 725. De temporum ratione..

However, Christianity of the Middle Ages was not conducive to scientific studies of nature. Any departure from the official interpretation of the Bible and therefore from the official explanation of the way the World is running was rapidly suspected of heresy.

The Arabic scholar Abu Yahya Zakariya’ ibn Muhammad al-Qazwini (1203 – 1283), tried to give the first scientific explanation. According to him, the tide was due to the thermal expansion of the water heated by the Sun and the Moon. However, his hypothesis could clearly not explain why the Moon played the most important role.

In the thirteenth century, Thomas Aquinas (circa 1225 – 1274) tries to reconcile science and religion: ‘Christians should not fear pagan philosophy, as any study of nature is the study of a work of God.’ For his part, he attributes the origin of tides to the Moon. In a typical Aristotelian fashion, he explains this phenomenon using the principle of sympathy between bodies: the water of the Moon draws water from the Earth.

The German astronomer Johannes Kepler (1571 – 1630) was convinced that the explanation of the tides would be sought in an attractive force of the Moon and the Sun. This force was to be some sort of magnetism. He was probably inspired by the recent discovery of terrestrial magnetism by the British physicist William Gilbert (1544 – 1603). This explanation is quite a good foreshadowing of the modern theory of tides! Simply, the attractive force behind tides is not magnetism but gravitation.

The physicist and Italian astronomer Galileo Galilei (1564 – 1642) said he was surprised that Kepler was interested in the action of the Moon on the water, to occult phenomena and other “childish things.” He himself believed, supporting Nicolaus Copernicus’ theory (1473 – 1543) of the rotation of the Earth, that tides were generated by the combined effect of the rotation of the Earth around its axis and its orbital motion around the Sun.

The entire “Day Four”, concluding Galileo’s Dialogue Concerning the Two Chief World Systems, published in 1632¹⁰G. Galilei, 1632. Dialogo sopra i due massimi sistemi del mondo. An English version can be found in: S. Drake, 2001. Dialogue Concerning the Two Chief World Systems, Modern Library., is dedicated to tides. Considering his theory of the tides as one of his major contributions, he had also planned to entitle the book “On Tides¹¹J.-M. Lévy-Leblond, 2009. Galilée et les marées : une fausse théorie fausse, La Recherche, n° 433, pp. 92 – 94..”

Overestimating the importance of the translation speed due to the description of the Earth’s orbit relative to the rotation of the Earth on itself, he explains the tides by the resulting acceleration and deceleration due to the combination of these two movements. The phenomena of neap and spring tides were, according to him, due to the pendulum system made by the Sun, the Earth and the Moon, which would mean that spring tides would occur only at new moon, while neap tides would only occur at full moon. This is in contradiction with observations. However, even if the rotation of the Earth is not at the origin of tides, it has an effect on the oceans and the atmosphere. I would address this in further articles.

Georges Fournier (1595 – 1652), chaplain of the Royal Fleet, demonstrates Galileo’s mistakes. In his book entitled Hydrographie, published in 1643¹²G. Fournier, 1643. Hydrographie, contenant la théorie et la practique de toutes les parties de la navigation, Chez Michel Soly., he explained the tides by the excitement of underground fumes under the action of the Moon and Sun. César d’Arçons (16.. – 1681), for its part, in Le Secret du flux et du reflux de la mer, et des longitudes, dédié à la sapience éternelle published in 1655¹³C. d’Arçons, 1655. Le Secret du flux et reflux de la mer, et des longitudes dédié à la sapience éternelle, L. Maurry., explains tides with back and forth movements of the Earth along the axis of the World. For his part, in his Traité des causes naturelles du flux et reflux de la mer published in 1680¹⁴C. Scalberge Minière, 1680. Traité des causes naturelles du flux et reflux de la mer, Claude Peigne & Étienne Massot, Charles Scalberge Minière attributes the expansion of seas to the Sun, the Moon acting as a mirror.

René Descartes (1596 – 1650), defended the idea of a lunar origin of tides. According to him, the Moon and the Earth are each surrounded by a great whirlwind. The pressure exerted on the whirlwind by the Moon was transmitted to the surface of the Earth and generated the tides.

The English mathematician John Wallis (1616 – 1703) in 1666 proposed an amended version of Galileo’s theory, seeking to include the influence of the Moon. He proposed to explain the oscillations of the tide not only by the movement of the Earth around the Sun, but also by its movement around the centre of gravity of the Earth-Moon system.

A very temporary conclusion

What will lay the foundations for the modern theory of ocean dynamics is the publication by Isaac Newton (1642 – 1727) in 1687 of the book Philosophiæ Naturalis Principia Mathematica¹⁵I. Newton, 1687. Philosophiæ Naturalis Principia Mathematica, Jussu Societatis Regiæ ac Typis.. With this work, he founded the classical mechanics. Of course, I will address this quite soon in this blog.

So, yes, Galileo was wrong about the tide. This does not diminish the importance of his work, standing at the epistemological rupture leading to modern science (which I detail in another article). Thus, all work in science at present is a consequence of his own work. Soon, I would also address the elements that have allowed him to be one of the instigators of this rupture.

Anyway, much of the research work is to be wrong. Contrary to what is sometimes said, science is not exactly about systematic doubt, which could lead to the pitfall of hyper-scepticism (this link leads to a French-speaking video), but about the search for errors: there are possible errors in the explanation of a given phenomenon and we try to correct them. So we try again the mistakes in the new explanation and so on, incrementally.

I consider the history of the study of the ocean dynamics interesting, and I think it was a good way to introduce some concepts related to my work. This is only the first part, I would shortly propose a further exploration of this history. It also highlights one important element: any research, however innovative it is, is always based on predecessors and is part of a long history.

These reflections conclude this post. I hope you have learned some new information. It opens the way for several other articles, which I will publish shortly.