Galileo Calls Out Chiaramonti's Manipulation of Data
Galileo's Dialogue, Day 3, Part 1
As I wrote in a recent post, I intend to write posts for each of the four days in the Dialogue Comparing the Ptolemaic and Copernican Systems1, the book that got Galileo in trouble with Rome. This is the first of three (I think!) posts about Day Three in the Dialogue. Here are the previous posts:
Day One: Galileo Dismantles Aristotle's Separation of Earth from the Heavens.
Day Two, Part 1: Galileo Attacks Aristotle’s Followers.
Day Two, Part 2: Galileo Insists the Earth is Spinning on its Axis.
Day Two, Part 3: Galileo on the Acceleration of Falling Bodies.
Day Two, Part 4: Galileo Channels Plato.
Day Three examines whether the Earth orbits around the Sun, as proposed by Aristarchus and Copernicus, or the other way around, as proposed by Aristotle and Ptolemy. The text is far more technical than that for the other three days, and warrants careful study. I think there will be three posts, this being the first.
Day Three begins with Salviati critically examining part of Scipione Chiaramonti’s De tribus novis stellis quae annis 1572, 1600, 1609 comparuere (About the three new stars that appeared in the years 1572, 1600, and 1609) (Cesena, 1628), in which Chiaramonti attempted to prove that the new star (supernova) discovered in 1572 in Cassiopeia constellation was in fact sublunar. This supernova is today called SN_1572. Chiaramonti was once praised in verse by poet Pier Francesco Minozzi as ‘‘the Aristotle of our times.’’
When this supernova appeared, a number of astronomers made observations and measurements of where it appeared in the heavens. An observer, at a specific location, with specific latitude, points his instrument to the Pole Star and measures the angle; from this angle, called the meridian altitude, the latitude of the observer can be computed. Then the instrument is pointed to the new star. If two different observers are observing at two different latitudes, then it is possible to estimate the distance to the celestial object from the parallax, i.e., the semi-angle between the two lines of sight to the object from the two observation sites.
Chiaramonti published his calculations of the distance to the new star, comparing twelve pairs of observations, and concluded that it was sublunar. It is precisely this conclusion that Salviati savages.
From the notes [pp.483-484] of Drake’s English-language translation of the Dialogue, we learn the names of these astronomers and the source for these observations:
Thirteen [astronomers] are named, but two of them (Peucer and Schuler) used the same data. Most of the figures given in the text came originally from Tycho [Brahe]'s Astronomiae instauratae progymnasmata (Uraniborg, 1602). [...] The observers mentioned, omitting Tycho..., are as follows:
Paul Hainzel, an amateur astronomer of Augsburg and a close friend of Tycho's. A famous quadrant 17 1/2 feet in radius which is said to have required forty men for its emplacement at Goeppingen, was employed by Hainzel for his observations.
Caspar Peucer, of Wittenberg, the son of a famous physician bearing the same name who corresponded with Hainzel and the Landgrave about the new star.
The Landgrave of Hesse, William IV, a famous patron of science and amateur astronomer.
Wolfgang Schuler, a friend of the younger Peucer, was a professor at the University of Wittenberg.
Thaddeus Hagek, physician to the king at Prague, wrote a book about this famous nova which was published at Frankfurt in 1574. It was Hagek who first acquainted Tycho with the manuscript in which Copernicus's system was circulated among the learned before publication.
Elias Camerarius, a professor at Frankfurt.
Adam Ursinus of Nürnberg, author of a number of astrological works, wrote of it in his Prognosticatio anni 1574; he believed this new star to be sublunar.
Jerome Muñoz, professor of mathematics and Hebrew at the University of Valencia.
Cornelius Gemma of Louvain, son of the eminent astronomer Gemma Frisius. Gemma wrote briefly on the nova during its first appearance in 1572, and afterward at length in his De divinis mundi characterismis (Antwerp, 1575).
Georg Busch, a painter and amateur astronomer of Erfurt, who argued that the nova was sublunar.
Erasmus Reinhold, son of the compiler of the famous Prutenic Tables (of planetary movements), was a physician at Saalfeld. Tycho exposed his appropriation without acknowledgement of the Landgrave's observations.
Francis Maurolycus, Bishop of Messina, one of the first to observe the new star.
Given all of the observations that Tycho published, Chiaramonti could have made calculations for many more pairs of observations. Salviati speaks:
These are twelve investigations which the author has made at his own choice from among the multitude which, as he says, could be made with the combinations of the observations of these thirteen observers; the twelve selected are, one may believe, those most favorable to his case.
Thus begins an exchange between Salviati and Sagredo:
Sagr: But I should like to know whether among all the other investigations, omitted by this author, there were any in his disfavor; that is, any from the calculation of which it would be inferred that the new star was above the moon....
Salv: Well, prepare not to hear, with unbounded astonishment, to what excesses of confidence in one's own authority and the foolishness of other people one may be carried by a desire to argue and to show oneself more intelligent than others.
Among the researches which the author has omitted, there are some which place the new star not merely beyond the moon, but even above the fixed stars. And these are not just a few, but the majority, as you see here upon this page where I have set them down.
Sagr: But what does the author [Chiaramonti] say about these? Or perhaps he has not considered them?
Salv: All too much has he considered them; he says that those observations are erroneous upon which such calculations are based as would put the star infinitely distant, and that these cannot be reconciled.
In today’s world, we could imagine Chiaramonti accusing all of these well-known astronomers of systematic experimental error, the catchphrase used to ignore a set of experimental results or observations that do not suit one’s favorite scientific theory.
Given that all of the astronomical observations differed, what technique was used by Chiaramonti to choose which were acceptable or not? He applied an “obvious” filter. If observations lead to obviously impossible conclusions, then these observations should be simply ignored. And just what are these obviously impossible conclusions? They are of two kinds: first, the new star is inside the Earth; second, the new star is at an infinite distance, or at least well above the known fixed stars.
Now it turns out that many of the observations lead to the conclusion that the new star was well above the known fixed stars, so Chiaramonti simply ignored these. But the obvious filter is deliberately biased in favor of his desired conclusion. For a very distant celestial object, a slight change in the observation, of a minute2 or even just a few seconds, might make one conclude that the object in question has moved from an infinite distance away to being among the fixed stars. On the other hand, for an object in sublunar space, even changing the observation by several minutes would not in any way change the conclusion that the object were in sublunar space. This is because the parallax for earthly observers for distant celestial objects is very small, so the slightest perturbation in the observation will lead to huge discrepancies in the conclusions. For near objects, the parallax is much larger, tolerating a significant error in observation without changing the conclusion. Salviati speaks:
Oh, but Simplicio, right here is your equivocation and author [Chiaramonti]'s — yours in one regards, and his in another. I see from your way of talking that you have the idea that the anomalies (esorbitanze) created in establishing the distance of the star increase in proportion to the instrumental errors made in the observations, and conversely that from the size of the anomalies one may deduce the size of the errors. Thus if it is said that from such observations the distance of the star is implied to be infinite, and therefore not subject to correction and accordingly to be rejected. The case is quite otherwise, my dear Simplicio. On account of your not having understood how matters do stand, I excuse you, as one untrained in such matters, but I cannot cloak the author's error under the same veil. He, pretending not to know this, and persuading himself that we would really not understand it, hoped to make use of our ignorance for boosting the stock of his doctrine among the multitude of the ill-informed. Therefore, for the information of those who are more credulous than well-informed, and to rescue you from error, know that it may be (and it happens more often than not) that an observation which gives you the star at the distance of Saturn, for example, with the addition or subtraction of a single minute of elevation to that taken by the instrument, will send the star to an infinite distance, and thus take it from the possible to the impossible. Conversely, in these calculations made from the observations which would put the star infinitely distant, the addition or subtraction of one single minute would often restore it to a possible location. And while I say one minute, a correction of one-half that, or one-sixth, or less may suffice.
Now fix it well in mind that at very remote distances like that of Saturn or of the fixed stars, the most trifling errors made by the observer with his instrument will change the location from finite and possible to infinite and impossible. It does not happen thus with distances that are sublunar, and close to the earth, where it may happen that an observation which implies the start to be, for instance, four radii distant, may be increased or decreased not merely by one minute but by ten, or a hundred, or even more, without the calculation rendering the star not only not infinitely distant but not even farther than the moon. From this you may see that the size of the instrumental errors, so to speak, must not be reckoned from the outcome of the calculation, but according to the number of degrees and minutes actually counted on the instrument. These observations must be called the more exact, or the less in error, which by the addition or subtraction of the fewest minutes restore the star to a possible position. And among the possible places, the actual place must be believed to be that in which there concur the greatest number of distances, calculated on the most exact observations. [pp.292-293]
Salviati then proceeds to show with a few calculations that the real outliers among the observations are not the ones that seem to indicate that the new star is at an infinite distance, but, rather, those that seem to indicate that the new star is sublunar. Salviati’s calculations show just how much in error all the other observations would have to be to accept as correct those observations indicating the new star to be sublunar. On the other hand, just slight adjustments to those observations indicating the new star to be at an infinite distance would suffice to make them realistic, showing the new star to be in the firmament with the known fixed stars.
The discussion with respect to the new star concludes with this exchange between Sagredo and Salviati:
Sagr: But if the matter is surrounded with so much confusion, uncertainty, and error, how does it happen that so many astronomers have so confidently declared the new star to have been very remote?
Salv: Either of two sorts of observations, both very simple, easy, and correct, would be enough to assure them of the star being located in the firmament, or at least a long way beyond the moon. One of these is the equality — or very slight disparity — of its distances from the pole when at its lowest point on the meridian and at its highest. The other is that it remained always at the same distance from certain surrounding fixed stars; especially x Cassiopeiae, from which it was less than one and one-half degrees distant. From these two things it may unquestionably be deduced that parallax was either entirely lacking, or was so small that the most cursory calculation proves the star to have been a great distance from the earth.
Given that Chiaramonti’s conclusions contradicted those of the most prominent astronomers of the day, how did he address this issue? He gave two reasons. First, the astronomers were misled because there was refraction that gave an erroneous measurement of the meridian altitude of the new star. Second, they misused the sextants with which they were making these measurements. Each of these completely fallacious arguments, ripped apart by Salviati, is really a claim that these astronomers were simply incompetent.
In other words, Chiaramonti was accusing the greatest astronomers of his time, including no less than Tycho Brahe, whose careful astronomical observations allowed Johannes Kepler to derive his laws of planetary motion, to be guilty of systematic experimental error. And Galileo Galilei publicly ridiculed Scipione Chiaramonti, the man who made this accusation.
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Galileo Galilei. Dialogue concerning the two chief world systems — Ptolemaic and Copernican. Translated by Stillman Drake, foreword by Albert Einstein. University of California Press, 2nd ed., 1967.
A circle is divided into 360 degrees, a degree into 60 minutes, and a minute into 60 seconds.