On Galileo's Method in the Dialogue
On Galileo's Method in the Dialogue
Galileo’s goal in the Fourth Day of the Dialogo [1], through the voice of Salviati, is to show how the earth’s mobility is required to adequately explain the phenomenon of tidal variation. One of his interlocutors, Simplicio, both denies the motion of the Earth and feels that the tides are already adequately explained. By the Fourth Day, Galileo feels he has already given ample evidence that the Earth moves, so much so that he makes it his chief assumption in explaining the tides. The Earth’s motion, however, is not all that Galileo requires. His account of what he calls the “primary and universal cause” of the tides depends upon an analogy with a moving barge, and from this analogy enters the requirement that the Earth’s motion causes an “uneven motion” on its surface that can explain the tides [1, pp. 444, 461]. Galileo’s arguments are complicated, and he does not follow a consistent method throughout the Fourth Day. There is a strong adherence to the power and necessity of observation, but also to the efficacy of thought experiment, analogy, and geometric demonstration. In what follows I will briefly outline some of the observations that are important to Galileo’s argument, and how he uses thought experiment and analogy to fit these observations to his theory of the tides.
Observation is crucial to many parts of Galileo’s argument. His account starts off with a description of what is known about the tides. First, tidal variation includes periodicities that are daily, monthly and annual. The daily periodicity is observed to have three varieties: vertical displacement of the water level alone, horizontal flow of water without any vertical change, and a combination of both vertical and horizontal displacement. By starting with these observations, Galileo rules out anything that does not account for this complexity, while considering what kinds of motion can create these same, visible effects. He rejects explanations offered by Simplicio on the grounds that we cannot recreate the mechanisms involved in such explanations using “appropriate artificial devices” [1, pp. 419-21]. We see here Galileo’s dual use of mechanical analogy and experiment: it serves both to offer a likely explanation of things and to rule out certain kinds of claims about the natural world. It is interesting to note here that one of Simplicio’s explanations, namely that the moon’s attractive force has something to do with the tides, was utterly rejected by Galileo, for the reason that although the moon traverses the entire Mediterranean, tidal variation is only visible in certain parts of the Mediterranean. For someone who appreciated the complex nature of tidal variation, this is a relatively thin response.
Galileo’s main argument for the “primary and universal cause” of the tides is based on the example of a barge abruptly changing its velocity [1, pp. 424-426]. Looking at his reasoning in this part of the Fourth Day is illustrative of the ways Galileo uses observation, thought experiment, analogy, and geometric demonstration to support a claim.
The ocean, where we see tides, is like a large vessel. Water in a vessel cannot move in as complex a way as it does with the tides unless the vessel itself moves. There are only two kinds of motion that can be applied to a vessel to create complex motions of water. The first occurs if parts of the bottom of the vessel were to move in opposing vertical directions, such as if the left side moved upwards and the right side downwards. The second kind of motion occurs if the vessel accelerates in some horizontal direction. Galileo cannot conceive of an Earth mechanism that could create the first kind of motion, so the second motion must be the cause of the tides. By analogy with the barges that come in and out of harbor holding water, we see the same complex motion of water when the barges change their horizontal velocity. This can be observed any time. But if this is the way the vessel must move to create the tides, then this horizontal, “uneven” motion must be attributed back to the Earth. This can be done by means of a geometric demonstration, which can be paraphrased as follows. When the Earth rotates while moving through its annual course, the part of it closest to the sun has a lower composite velocity than the part of it farthest from the sun. That is, at the farthest point, the diurnal, rotational velocity and the annual velocity adds constructively, while at the closest point they add destructively. But in a half day’s rotation, the furthest and closest parts of the Earth swap, so to explain this change in velocity, an acceleration must have occurred. It is this acceleration that we match, by analogy, to the same acceleration we see in a barge that causes its water to rise and fall just like the tides.
Galileo’s argument is more complex than how I have described it, since it must also explain regional factors as well as the monthly and annual components of the tidal variation. But he says on many occasions that the analogy with a vessel on a barge explains the primary cause of the tides. This is a thought experiment insofar as he did not go out and measure the barge itself, the size of the vessel, the amount of water displaced in the middle and on the sides, but he describes what would happen and then urges the reader to go see for herself. He uses a geometric argument to both aid the reader and lend credibility to his method.
There are other noteworthy references to experience and analogy throughout the Fourth Day. For instance, to explain regional variations, he notes that the Red Sea, where apparently there are no tides, is shaped diagonally from northwest to southeast, which does not allow for such a buildup across its east–to–west dimension. He supports this with an account of how a vessel’s depth and breadth affect the amplitude of the vertical and horizontal displacements witnessed. He also gives an account of why smaller bodies of waters, such as lakes, do not exhibit tidal variation. To explain the monthly variation in the tides, he compares the moon to a weight on a pendulum which, when slid along the axis of the pendulum, modifies its period and can thus lead to additional accelerations. To the objection that there would be an immense wind, at the very least along the smoothest parts of the Earth’s surface such as the open ocean, Galileo first argues that wind does not “preserve disturbances” as well as water, as is clear if we notice that water on a lake continues to move well after the wind that has produced it has subsided [1, p. 437]. He next argues that there is, in fact, proof for such a wind, which Sagredo supports with the statement that he has recorded the travel times of many ships and finds that ships traveling east to west go, on average, faster than those traveling west to east. With these examples, we see the imagination of Galileo at work, his adherence to a disciplined approach to observation that appreciates complexity, and his use of analogies with phenomena that are better understood in order to support his argument for the tides.
There are two minor remarks I want to make on issues related to Galileo’s method in the Fourth Day. First, it is worth considering what he accomplishes by presenting his arguments as through a dialogue between a layman, an Aristotelian, and a stand-in for himself. There is not enough room to explore this here, but I believe that the dialogue form helps Galileo do two things. First, it makes the work more readable and approachable to a wider audience, and thus popularizes its Copernican views. Second, it allows Galileo to prop up Simplicio as a straw man for Aristotelian objections to his argument. The objections raised by Simplicio can be tailored by Galileo however he likes, and provide him with a way to make his own arguments look all the more correct.
The second remark I would like to make is that Galileo twice mentions that he is opening up a portal: “what I am about to say, I propose merely as a key to open portals to a road never before trodden by anyone,” and, later, “you have done a great deal by opening the first portal to such lofty speculations” [1, pp. 418, 461]. Although Galileo makes it clear that the primary cause of the tides has been well established in the uneven motion of the Earth caused by its diurnal and annual movement, he believes that the complexity of the phenomenon is such that others will be able to refine what he has said. Galileo thus sees himself as a disruptor of the old system, paraphrased in the words of Simplicio, and offers a starting point for further inquiry. Our current understanding of the tides is so different from Galileo’s—indeed, it is closer to Simplicio’s prelate who claims that “the moon, wandering through the sky, attracts and draws up toward itself a heap of water which goes along following it” [1, p. 419]. Therefore, I would be interested to learn how the argument in the Fourth Day was received, and how it challenged others to examine the phenomenon more closely. By offering a likely account, and opening a portal, Galileo may have inspired others to think more critically, and thus come to a more refined understanding.
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