Strange Tales of Galileo and Proving: Omitted Data and the Tides

Last week I wrote a post on how even books for children and travel books state (incorrectly) that Galileo proved that the Earth circles the sun, as Copernicus had said it did.  This post tells a strange story about Galileo’s efforts to prove that the Earth circles the sun.

In Galileo’s time, no telescopic observation was likely to prove Earth’s motion.  Before the telescope had even been invented, Tycho Brahe had proposed a geocentric theory in which the planets circled the sun while the sun, moon, and stars circled the Earth.  Brahe’s theory was mathematically and observationally identical to Copernicus’s heliocentric theory insofar as the Earth, sun, moon, and planets were concerned: the “machinery” of both systems was the same, it was just that in Brahe’s the Earth stood still, whereas in Copernicus’s the sun stood still.  Galileo’s telescopic observations proved that Venus circled the sun—but Venus circled the sun in both Brahe’s geocentric theory and in Copernicus’s heliocentric theory.  Technically, observations of the stars could prove one theory over the other, because in Copernicus’s theory Earth moved with respect to the stars, whereas in Brahe’s it did not.  However, Copernicus had specified that the stars were so far away in his theory that the Earth’s motion was nothing by comparison, and so observing the stars would not reveal Earth’s motion.

The Tychonic geocentric (left) and Copernican heliocentric

The Tychonic geocentric (left) and Copernican heliocentric (right) theories.

With astronomical observations being no help, Galileo looked for proof of Earth’s motion in a common Earthly phenomenon: the tides of the ocean.  The level of the ocean rises and falls every day at beaches and harbors on seacoasts everywhere.  Galileo argued that this rising and falling—the tides—was evidence of Earth’s motion.

Consider:  What are the oceans but giant basins filled with water?  What are seacoasts but the edges of those basins?  Now, how do you make water in a basin rise and fall along the edges of the basin?  There is only one way to do this: you make the water rise and fall by moving the entire basin unevenly; that sloshes the water back and forth, causing it to rise and fall at opposite edges of the basin!  Put a basin of water on the floor of your car; then step on the gas, and then the brake, and then the gas, and so on; the water will slosh everywhere.  If, on the other hand, the car just sits (or even moves at a steady speed in a straight line), and you don’t touch the water, that water will just sit in the basin.

Well, said Galileo, in the heliocentric theory the ocean basins move unevenly, going faster and slower and faster again, just like in your car.  In the heliocentric theory the Earth rotates once per day.  The Earth measures 25,000 miles in circumference, and if the Earth rotates then people at the equator travel all the way around the Earth in 24 hours.  Thus the equator, and the people and waters at the equator, moves at 25,000 miles/24 hours = 1000+ mph.  Moreover, in the heliocentric theory, the Earth orbits the sun, and the orbital speed is almost 70,000 mph.  So imagine that the Earth orbits the sun clockwise, and rotates clockwise, as shown below (the blue arrow shows the Earth’s orbital motion; the red arrow shows the Earth’s rotational motion).

At point A on the side of Earth opposite the sun (the midnight point), the 1000 mph of rotational speed is in the same direction as the orbital speed; at point B on the side of the Earth facing the sun (the noon point), the 1000 mph of rotational speed is opposite the orbital speed.  So, A is moving clockwise around the sun at 70,000 + 1,000 = 71,000 mph, and B is moving clockwise at 70,000 - 1,000 = 69,000 mph.  Therefore a person on the equator is hurtling round the sun 2000 mph slower at noon than at midnight!  Therefore, from noon to midnight that person speeds up by 2000 mph,* and from midnight to noon that person slows down by 2000 mph.  And so do the ocean basins!

Voila!—uneven motion.  This uneven motion must slosh the water in the oceans, causing the tides.  All this Galileo described in a January 1616 letter to a Cardinal Allesandro Orsini (put your usual image of a Roman Catholic Cardinal out of your mind—Orsini was born in 1593; he wasn’t 25 years old at the time).

There seemed to be one problem with all this:  If this uneven motion was the cause of the tides, then the oceans should slosh toward one direction on account of the noon-to-midnight speed-up, and toward the other direction on account of the midnight-to-noon slowdown.  There should be one “up slosh”, or high tide, and one “down slosh”, or low tide, each day.  Thus there should be twenty-four hours between one high tide and the next, and twelve hours between high and low tides.  But in the Mediterranean Sea there are two high tides and two low tides each day, and therefore six hours between high and low tides.

Galileo said that, actually, this was not a problem.  The six-hour period is the result of a secondary effect, he said, namely the water rebounding off the eastern and western ends of the Mediterranean Sea, and the “slosh” being sent back across that sea.  In other words, while the Earth’s heliocentric uneven motion drives the tides, the Mediterranean’s six-hour period is an effect of the length of the Mediterranean.  In the larger Atlantic Ocean, Galileo said, the tide period is twelve hours.  Here are his words on the matter:

[T]he approximately six-hour period commonly observed is no more natural or significant than any other; rather, it is the one which has been observed and described more than others, since it takes place in the Mediterranean Sea around which all our ancient writers and a large part of the moderns have lived.  The length of this Mediterranean basin is the secondary cause that gives its oscillations a six-hour period; whereas on the eastern shores of the Atlantic Ocean, which extends to the West Indies, the oscillations have a period of about twelve hours, as one observes daily in Lisbon, located on the far side of Spain; now, this sea, which extends toward the Americas as far as the Gulf of Mexico, is twice as long as the stretch of the Mediterranean from the Strait of Gibraltar to the shores of Syria, that is, 120 degrees for the former and 56 degrees for the latter, approximately.  Thus, to believe that tidal periods are six hours is a deceptive opinion and it has lead writers to make up many fictional stories. [He then goes on to discuss how complex the tides get within portions of the Mediterranean.]

If you have any familiarity with Atlantic Ocean tides, O Reader, you immediately recognized the “strange” part of this tale.  The business about an Atlantic Ocean twelve-hour period between tides is bogus.  The period is six hours in the Atlantic.

Somewhere along the line Galileo learned he was wrong about the Atlantic tides.  The historical record shows that at least by 1619 he was told of this, as one Tobie Matthew reported as much in a letter to Francis Bacon.  And Galileo, in his 1632 Dialogue Concerning the Two Chief World Systems—Ptolemaic and Copernican (sixteen years after his letter to Cardinal Orsini), omits all mention of the Atlantic, and still sticks with the idea that the six-hour tide period is a characteristic of the Mediterranean.  What Galileo says in the Dialogue is—

Six hours, then, is not a more proper or natural period for these reciprocations than any other interval of time, though perhaps it has been the one most generally observed because it is that of our Mediterranean, which has been the only place practicable for making observations over many centuries. [He then again goes on to discuss how complex the tides get within portions of the Mediterranean.]

So much for Lisbon, the 120 degrees and the 56 degrees, and all that.  From a scientific perspective, this seriously un-cool.  When I am teaching my students how to perform physics experiments, I always emphasize that one cannot selectively choose one’s data.  If you are measuring the acceleration due to gravity by timing the fall of a ball, and not all of your times are in agreement, you cannot just ignore the ones you don’t like.  You have to report all the data you have, both the data you like and the data you don’t like.  You can then try to explain away the data you don’t like, if you think you have good reason to do so, but you cannot just leave it out.

And in the end, leaving out the Atlantic Ocean did not make the problem of the tides period go away.  Consider, for example, the Church officials who investigated the Dialogue (the Dialogue is the book that Galileo was put on trial for) after it was published.  After describing Galileo's tides theory one official wrote:

However, he does not untangle the difficulty that, given this doctrine, since the change between greatest acceleration and maximum retardation of the earth’s motion occurs at twelve-hour intervals, then high and low tides should also occur at twelve-hour intervals. But experience teaches that they occur every six hours.

In science, it never pays to leave out the data.  It was strange, and un-cool, that Galileo did that while trying to prove that the Earth moves.

*You would not feel a gain of 2000 mph in 12 hours.  That’s 2000/12 = 167 mph in an hour, or a little over 80 mph in 30 minutes. Even a fairly sluggish automobile can easily accelerate to 80 mph in well under one minute.

P.S. We now understand the tides to be a result of the gravity of the sun and the moon, not of the Earth’s motion.



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Strange Tales of Galileo and Proving: Omitted Data and the Tides — 1 Comment

  1. Pingback: Whewell’s Gazette: Year 3, Vol. #32 | Whewell's Ghost

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