Christian Waldvogel

Following Galileo’s conviction in 1633, the protagonists of his Dialogue Concerning the Two Chief World Systems gathered to discuss a theory of how Galileo Galilei could have evaded the guilty verdict.

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Works in Catalogue
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5 lightboxes, C-print on Duraclear on acrylic glass, LED, aluminum, Dibond, 1186 × 1186 × 44 mm each,
Edition of 5
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created 2010-05-05 | last update 2008-11-25 | Copyright (c)2002–2010 by Christian Waldvogel

Galileo's Missing Argument

Part 1: The Dialogue

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In 1632, Galileo Galilei published his Dialogue Concerning the Two Chief World Systems in which he juxtaposed the two most prominent world systems being debated at the time: the geocentric Ptolemaic, and the Copernican system, according to which the Earth revolves around the Sun and not the other way round.

The Dialogue takes the form of a discussion between the philosopher Salviati,1 who argues in favor of Copernicus, the impartial layman Sagredo,2 and the peripatetic Simplicio,3 who represents the world views of Aristotle and Ptolemy.

1 — Salviati is modeled on Galileo’s friend Filippo Salviati (1582–1614) and is characterized as a scientifically educated, rational person, who espouses Galileo’s views.

2 — Sagredo is named after the Venetian mathematician Giovanni Francesco Sagredo (1571–1620), who was also a close friend of Galileo’s.

3 — Simplicio is ostensibly named after Simplicius of Cilicia, a sixth-century commentator on Aristotle, and hence an opponent of Copernicus. Since «Simplicio» sounds very similar to «semplice» (Italian for «simple-minded»), it seems likely that the name was also a double entendre intended to signal Galileo’s rejection of the Ptolemaic model.
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As the discussion progresses over a period of four days, Simplicio becomes increasingly ensnared in contradictions, while Sagredo tends to support Salviati, who generally has the better arguments.

Having been encouraged by Pope Urban VIII to publish a book about the two chief world systems, but without arguing in favor of either one of them, Galileo made a show of balancing all the arguments. He even concluded the work with Urban’s own favorite argument4—articulated (unfortunately) by none other than Simplicio.

4 — Urban VIII liked the argument that a theory could never be proven using the effects the theory predicts, since God could invoke such effects at any time using other means.
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Only a few months after the Dialogue was published, Galileo was ordered to stand trial before the Inquisition on a charge of heresy. In June 1633, he was tried by the Inquisition and forced to renounce his views. H e was found to be «vehemently suspect of heresy»5 and his Dialogue placed on the Index of Forbidden Books. Rumor has it that he left court murmuring: «eppur si muove!»6

5 — The sentence basically fell into three parts: First, Galileo was found guilty of having asserted that the Sun is the motionless center of the universe, that the Earth is not the center of the universe, but is itself moving, and that one may hold and defend an opinion as probable, even after it has been declared contrary to Holy Scripture—whereupon he was ordered to «abjure, curse, and detest» the said opinions. Second, he was sentenced to imprisonment, although this sentence was later commuted to house arrest.Third, the offending Dialogue was banned and the publication of any other works by him—including all future works—prohibited, although this was not announced until after the trial.

6 — And yet it moves!
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What is not widely known is that in the eighteenth century, an Italian theologian and historian7 found a manuscript of a postscript to the Dialogue in the estate of Galileo Galilei. Boldly transplanting his scientific work into the domain of fiction, Galileo here adopts a method previously used by Dante Alighieri.8 By explicitly introducing himself as a protagonist, he succeeds in blurring the boundaries between reality, theory, and fiction.

7 — Giorgio Ursinus Pulviscolo, 1650–1735

8 — Galileo was an admirer of Dante’s Divine Comedy and once presented a topographical study of Dante’s Inferno at the Accademia Fiorentina. He shares with Dante the honor of being the first Italian author to write a major work in his field in the Italian vernacular, and thus of addressing not only an educated elite proficient in Latin, but the general public as well.
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The postscript describes a second meeting of Salviati, Sagredo, and Simplicio which must have taken place in the late summer or fall of 1633. Having heard that Galileo has been condemned for publishing a transcript of their first discussion, they weigh up the arguments that might have prevented him from having to stand trial for heresy.

While Salviati and Simplicio hold on to their established positions, Sagredo now plays a much more active part in the discussion. In a clear departure from his previous role as a by and large neutral interlocutor for Salviati and Simplicio, he now propounds an audacious theory of his own.

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Part 2: The Redefense

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Rewritten and edited passage from Galileo’s manuscript
«The Second Meeting of the Philosophers Discussing the Two Chief World systems»

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Salviati:

Dear colleagues, I gather you have heard the sad news of Galileo Galilei’s conviction?

Simplicio:

I have indeed, and I’ve heard that you, Signore Sagredo, know how Galileo could have avoided conviction?

Sagredo:

Well I do have a few ideas. As Galileo mentioned in the foreword to our first Dialogue,9 one would have to leave the Earth, and look at it from beyond in order to see, and thus prove, that it does not remain motionless at the center of the universe.

9 — See Galileo Galilei, Dialogues on two world systems, 1661, translated by Thomas Salusbury, p.5: «I will endeavour to shew that all Experiments that can be made upon the Earth are insufficient means to conclude it’s [sic] Mobility [...]»
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following images: [ figs. 3–6 ] THE EARTH FROM THE MOON AT TAURUS-LITTROW:
— June 14, 1633, 00:48 UTC
— June 14, 1633, 04:54 UTC
— June 14, 1633, 01:58 UTC
— June 13, 1633, 02:07 UTC

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Simplicio:

So Galileo should have taken the Inquisition to the Moon?! And how would such a voyage have helped him to explain Copernicus’ theory, disprove Ptolemy’s, and thus exculpate himself? Can you enlighten me on this point, Signore Sagredo?

Sagredo:

When we look at the Moon from the Earth, we see it move across the sky, always showing us the same face. If, on the other hand, we were observing the Earth from the Moon, we would see it standing still at the same point in the Moon’s sky, which in turn would depend on where on the Moon we were standing. Would you agree, Signore Simplicio?

Simplicio:

Yes, I would. But this is just further proof of the ingenuity of Aristotle!

Sagredo:

I’m not so sure; because if Copernicus were right, and the Earth does indeed rotate around its own axis, then we would see this from our vantage point on the Moon. Let us suppose that, contrary to what Aristotle says, it takes twenty-four hours for the Earth to revolve around its own axis. That being the case, a time span of just a few hours would be enough to reveal this rotation to us. This in turn would prove that the succession of day and night is a consequence of the rotation of the Earth, and not of the Sun circling the Earth.

If, moreover, the Earth does indeed revolve around the Sun, as Copernicus and Galileo have argued, then the terminator10—the line which separates day and night—would have to move as well, albeit only very slowly in relation to the speed with which the Earth itself turns.

10 — Seen from the Moon, the movement of the Earth’s terminator is a function of the Earth’s revolution around the Sun and the Moon’s revolution around the Earth.
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Third, we would notice the shadows that we ourselves were casting on the Moon moving almost synchronously with the Earth’s terminator.11 We would have to invest more time in this last observation than in the first two, since it deals with the annual revolution of the Earth around the Sun and the monthly revolution of the Moon around the Earth. The time span needed to render the relevant aspects discernible to the eye would therefore be longer.

11 — The apparent movement of the Earth’s terminator is the sum of the components stemming from the Earth’s revolution around the Sun (0.041° per hour) and the Moon’s revolution around the Earth (0.549° per hour): 0.59° per hour. The movement of the Moon’s terminator consists of the second component only, and is therefore ten times faster.
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[ ﬁg. 6 ]

The Earth from space as seen from the departing MESSENGER spacecraft heading for Mercury. The series covers a time span of four hours with one hour elapsing between each image and the next. The initial and previous states of both a reference point on the Earth and the night-day terminator are marked in white, their current states in red.

The difference in speed between the rotation of the Earth (which completes a whole cycle in 24 hours) and the movement of the terminator (which takes one year to complete a whole cycle), is easily discernible, though the movement of the terminator visible here is, in fact, also due to the changing vantage point aboard the spacecraft. The shift caused by the Earth’s path around the Sun alone would be much smaller.

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From these three observations, we would be able to deduce not only that the Earth rotates around its own central axis (which we would be able to see), but also that, together with the Moon, it revolves around the Sun.

In addition, we would be able to see that the Earth rotates around an axis which is tilted relative to the Sun, and by observing the shapes of the landmasses and the seas, would soon realize that this axis runs between the two main poles of the compass: north and south.

Simplicio:

That’s an interesting argument, although I still have my doubts. But setting all this aside for a moment, perhaps you could explain to me how Galileo, standing on the Moon, would have been able to see the Earth in sufficient detail to be able to make out the seas and continents looming up from behind the horizon on the left, passing through the illuminated portion, and then disappearing again into the night?

Salviati:

Doubtless you will have seen the images of the Moon that Galileo drew looking through the telescope of his own construction?12

12 — Simplicio had probably not seen these drawings, since he was modeled in part on Cesare Cremonini, a colleague of Galilei’s who had refused to look through the telescope.
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Sagredo:

That is exactly what I was going to mention, Signore Salviati. The Moon is much smaller than the Earth, because the Earth is the planet and the Moon only its satellite. If we were to gaze at the Earth from the Moon, it would look three times larger than the Moon does seen from the Earth. Using Galileo’s telescope it would be easy to distinguish the Earth’s features—and in great detail, too, as even you must admit, Signore Simplicio.

Simplicio:

Well yes, but all this would prove only that the Earth rotated around its own axis, not that it revolved around the Sun! Would it not be truer to the logic and indeed the sense of both Aristotle and Copernicus to say that the reality we perceive contains aspects of both theories?

Salviati:

It might indeed be truer, but the logic and sense which you speak of and which have always been at the heart of Aristotle’s works require that reality be explained by a single theory—a theory which builds on the same principles for all timescales and all orders of magnitude.

Sagredo:

I tend to agree with both of you, but allow me to propose the following argument, which is actually a continuation of the ideas I presented previously: If we looked at the Earth from the Moon over a period of a few months or a year, we would see the Earth—which one would expect to remain in the same place—move a few degrees across the sky. If we then plotted the Earth’s position, we would see the diagram of a highly complex movement evolving before our eyes.

Now, if we were to argue along the lines of Signore Simplicio and were to maintain that whatever we see moving is indeed moving, we would be bound to conclude that the Earth is tumbling about in space. But as I’m sure you would agree, Signore Simplicio, this would be at odds with both Ptolemy and Copernicus, as well as your own personal opinion.

On the other hand, I imagine that no one would oppose me if I were to assert that the Moon orbits the Earth. Our pattern could therefore be explained using the notion that the Moon orbits the Earth on a path which is neither aligned to the Earth’s center and equator, nor exactly circular.

In other words, it could be argued that it was our own movement—the Moon’s in this case, since that would be our vantage point—that was causing the heavenly body we observed to move.

Simplicio:

So further proof for Aristotle!

Salviati:

Not quite! Because we would have seen with our own eyes that the Earth turns, and would thus have disproved the assertion you made in our first discussion,13 in which you argued that the 24-hour cycle of the Sun and planets was a consequence of the movement applied to them by the uppermost celestial sphere, which is also alleged to be moving, although its existence you have merely hypothesized. But let’s allow Signore Sagredo to continue his most persuasive argument.

13 — See Galileo Galilei, Dialogues on two world systems, translated by Thomas Salusbury, 1661, p.104:
SAGR. I would have you tell me in the third place, whether you believe that the Moon and the other Planets and Cœlestial bodies, have their proper motions, and what they are.
SIMPL. They have so, and they be those according to which they run through the Zodiack, the Moon in a Moneth, the Sun in a Year, Mars in two, the Starry Sphere in those so many thousand. And these are their proper, or natural motions.
SAGR. But that motion wherewith I see the fixed Stars, and with them all the Planets go unitedly from East to West, and return round to the East again in twenty four hours, how doth it agree with them?
SIMPL. It suiteth with them by participation.
SAGR. This then resides not in them, and not residing in them, nor being able to subsist without some subject in which it is resident, it must of force be the proper and natural motion of some other Sphere.
SIMPL. For this purpose Astronomers, and Philosophers have found another high Sphere, above all the rest, without Stars, to which Natural agreeth the Diurnal Motion; and this they call the Primum mobile; the which carrieth along with it all the inferiour Spheres, contributing and imparting its motion to them.
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sagredo:

We’re actually almost through. If we were to plot the path of the Sun across the Earth’s sky for a similar period of time, we would observe a similar pattern, occurring synchronously with the change of seasons—the fact that in summer the Sun rises higher than in winter.

The Earth's path as seen from the Moon 1533-1633

[ ﬁg. 8 ]

The apparent movement of the Earth as seen from the Moon in the years 1533–1633. The viewing point is Mons Hadley Delta, the landing site of Apollo 15. The diagram was deskewed to make up for the distortions caused by perspective. Plotted using a custom script and freeware astronomy software (Celestia).

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Having seen from our previous observations that the Earth revolves around a tilted axis, we would be able to explain the Sun’s seasonal pattern as a consequence of this same axial tilt, which does not change its orientation during the Earth’s orbit around the Sun.

Here again, the explanation of the perceived movement lies in the observer’s own movement! Surely you would both concur that even according to Aristotelian logic, these similar effects are best explained by similar causes?

A few months later, Simplicio received a package sent to him by Sagredo, who in the meantime had returned to Venice. The pallium it contained had been embroidered with that very same diagram of the Earth’s apparent movement that had finally convinced Simplicio of the Copernican world model.

The letter stated that the simple, but precious pallium had been made in the Sciabbo manufactory14 using only the finest wool, that the diagram had been plotted for the years 1533 to 1633,15 and that both Salviati and Sagredo hoped that Simplicio would pardon the offenses that Galileo had occasioned him in the first dialogue, and use his influence to help Galileo out of his predicament.

14 — Marco Sciabbo was the most prominent woolen cloth tailor in seventeenth-century Venice.

15 — 1533–1633 is the time span during which the Roman Catholic Church knew of the Copernican world model, ending with the year in which Galileo Galilei was sentenced for defending it.

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Part 3: Epilogue

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One question remains, however, and that is this: How do we know that the images in [ figs. 3–6 ] show exactly what Galileo would have seen if he had taken the Inquisition to the Moon?

According to the prevailing theory, the Moon was formed around four and a half billion years ago when Proto–Earth collided with a body the size of Mars, commonly referred to as Theia.16

16 — The Theia hypothesis (or giant impact hypothesis) is supported by findings made using Moon samples collected by the Apollo astronauts.
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Debris from the collision rained down onto what was left of Theia, gradually accreting to form what today is the Moon. The shower continued for millions of years, creating the craters that Galileo had seen through his telescope. While other impacts of a much smaller magnitude have continued to shape the Moon’s surface in the course of time, these have been few and far between compared to the massive bombardment that marked the beginning of the Moon’s existence as the Earth’s satellite.

Statistically speaking, the probability that a major impact has occurred in the time since Galileo made his observations is very small, and that such an impact has occurred in the time since the Apollo astronauts walked on the Moon even smaller. It can therefore be argued that today, the Moon looks exactly as it did 40 years ago, and even 400 years ago .

As the Moon orbits the Earth and these two bodies revolve around the Sun, the Moon’s surface is illuminated at the same angle once every month.17 We can therefore calculate many alternative capture dates for every picture taken on the Moon.18

17 — Once every 29.530 days to be precise. This interval is called a sidereal month.

18 — This of course holds true only if the images do not show mobile, artificial objects, and/or astronauts.
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In the course of their six landings on the Moon, the Apollo astronauts walked on much less than a hundredth of a millionth of the Moon’s surface;19 it could therefore be argued that the Moon is essentially untouched.

19 — The twelve astronauts who walked on the Moon covered a total distance of 89.95 km and actually set foot on an area of less than one square kilometer.
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[ ﬁg. 11 ]

Map of Mons Hadley Delta, the area of the Moon where the photograph in [ ﬁg. 10 (above) ] was taken. The cone of vision for this image is indicated, as are the paths which the astronauts took on foot and in the Lunar Roving Vehicle. The spot where the astronauts stepped into the cone of vision and where their footprints would be visible is more than four kilometers away from the viewing point. Whatever traces they left would therefore be much too small to be discernible, especially as the photograph was taken from chest height and hence at a low angle.

The photographs taken were centered and exposed to show as much foreground detail as possible; because of this, the Earth tends not to be in the frame at all, nor are there any stars visible in the black sky.20

20 — [ See also Space from Space ]
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The images shown in [ figs. 3–6 and 10 ] were composed using original NASA material, and then reassigned to a possible capture date shortly before Galileo’s trial. The stars as well as the position and orientation of the Earth were simulated using astronomy software and integrated into the sky.

These pictures represent the first photographs ever taken—in 1633.

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[ ﬁg. 12 ]

Clipping from Time Magazine, March 12, 1984.

From The Times Online

November 26, 2008

Vatican seeks to rehabilitate Galileo Galilei. The full record of the 17th-century trial of Galileo Galilei for heresy may be published as a part of the astronomer’s rehabilitation.

From The Times Online

January 29, 2009

Catholic Church abandons plan to erect statue of Galileo. Plans to complete the Catholic Church‘s rehabilitation of Galileo by erecting a statue of him in the Vatican grounds have been shelved indefinitely.

It was not until 1835 that the last vestiges of official Catholic opposition to heliocentrism disappeared, and even as late as 1990, Cardinal Ratzinger, who would later become Pope Benedict XVI, claimed that current views on the Galileo affair were «a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science, and technology goes today.»

To what extent this can be taken to imply that observing an external process requires a rethink not just of the process observed, but of the observer as well, remains an open question.

[ ﬁg. 13 ]

Pope Benedict XVI receives the festive pallium just before the rehabilitation ceremony held for Galileo at the Vatican.