Previously: Part 8, Trial and Error
From Plausible to Proven
Galileo’s book “proved popular amongst literati who were not astronomers [and] who enjoyed his very obvious polemic writing skills; but contrary to popular opinion it didn’t play a significant role in the contemporary scientific discussion.” (Christie, Galileo’s great bluff 2010) One could even make an argument that Galileo managed to delay acceptance, although TOF does not do so.
What it came down to is that the issue would not be settled by astronomical mathematics, but by a new physics.
Please Help Me, I'm Falling....
The objections to geomobility on the part of the physicists were manifold, but because the old physics is gone, Patient Reader will blink in astonishment at some of the objections and a little thought-balloon reading WTF? will form over his or her noggin. For example, heavy bodies will in the common course of nature fall toward the center of the world. If the Sun were in the center of the world, cannon balls dropped from the tower of Pisa would fly off toward the Sun; but we see that they do not, therefore etc. Us Moderns in our wisdom are left scratching our collective heads and saying Really?
Other objections made more sense, in that we can understand why people would have raised them.
|Those headwinds sure are strong!|
- If the world is turning at a high rate toward the east, why is there no steady breeze coming from the east? This is a sort of ancient Michelson-Morley experiment.
- If the earth is whipping around the sun, why isn't the Moon left behind? (Or the oceans and the atmosphere?)
Of course, there were answers to these, even then. "Common motion" asserts that the air shares the earth's rotation, and therefore there would be no particular east wind. And the moons of Jupiter showed that, whether we knew why or not, moons are not left behind as their planet moves.
|As the earth revolves, the relative positions of the stars|
- If the earth were whipping around the sun, we should see parallax among the fixed stars, but do not. The Copernicans answered, "Well, yeah, but maybe the stars aren't just far away but really really far away." But you cannot save an unproven hypothesis by asserting a second unproven hypothesis. The stars had to be relatively close because otherwise their observed diameters would mean they were ginormous entities. Some Copernicans embraced this and said "Goddidit!" Who cared how enormous the stars were, since God was infinite.
|As the earth turns a ball at the top of the |
tower has a greater eastward velocity
and will fall east of the plumb line
- If the earth were rotating, objects at the top of a tower would have a greater eastward motion than those at the bottom of the tower; and therefore, a dropped object would not only fall but move eastward realtive to the tower. No such deflection is observed. "Well, yeah," said the Copernicans, "it's probably a really small deflection that falls within the error of measurement."
The problem of history, John Lukacs used to tell us is that we "must consider the battle of Salamis as if the Persians might still win." Meaning that you want to understand what happens in 1633, you can't consider things learned in 1687 or 1803. The mid-17th century had no clear concept of inertia, of gravitation, of forces, etc.; and while ontologically there may still be no clear concept of these (and therefore we are blind to the foolishness over which our descendents will one day mock us) the same is certainly true of 380 years ago. After all, the classical, medieval, and Renaissance folks laughed at the ancient belief that the world was flat. (The Chinese at this point still did believe.) But because Aristotle had demonstrated that the world was a sphere, the Scriptural passages describing the sky as a tent pitched over a flat earth were no longer understood as literal.
What was needed now was a new theory of motion.
Just Dropped in to See What Condition My Condition was inA new theory of motion was already in development. Aristotle had declared that heavier bodies would fall faster than lighter bodies. But Albrecht of Saxony described a thought experiment in the 14th century in which he imagined two equal-sized falling bodies attached by a string, and then mentally cutting the string. It was absurd to imagine the two separate bodies would suddenly decelerate to half speed. Thomas Bradwardine and the Merton Calculators proved the Mean Speed Theorem and described the free fall of bodies. Doubts about Aristotle's physics began to circulate.
1543 Benedetto Varchi publishes a book listing experimental evidence from Francesco Beato and Luca Ghini contradicting Aristotle's view of free fall.Aristotelian physics was tottering well before Galileo took up a sledge hammer.
1544 Domingo de Soto, a Dominican philosopher, publishes a book with the first correct statement of the law of free fall.
1570 In Opus novum de proportionibus, Girolamo Cardano, demonstrates that two balls of different sizes will fall from a great height at the same time.
1574 Girolamo Borro, one of Galileo's teachers, describes experiments repeated several times where a wooden and lead ball were thrown out of a high window and the wooden ball reached the ground first.
1575 Guiseppe Moletti, Galileo's predecessor at University of Padua, drops balls of the same volume but different materials and of the same material but different weights and discovers they hit ground at same time.
1585 Flemish Scientist Simon Stevin conducts an experiment dropping two balls, one weighing 10 times the other from 30 feet and discovers that they reach ground at same time.
1632. Bonaventura Cavalieri publishes Specchio Ustoria (On Burning Mirrors). Otherwise a book about mirrors, it's the first book to describe the parabolic nature of projectile motion. Both Thomas Harriot and Galileo Galilei had described this motion before Cavalieri, but in private notes never published. Well, Harriot never published nothing, but Galileo was not one for staying mum. Projectile motion does not sound very heliocentric, but folks are creeping up on a calculus of motion. For all practical purposes, up to now mathematics basically consists of arithmetic and geometry, with geometry having pride of place. No wonder Aristotle thought mathematics was unsuited to physics, which involved changeable matter.
Meanwhile, Back at the Glass...Late 1632. Leander Bandtius, Abbot of Dunisburgh, (and owner of a particularly fine telescope) notes a large red spot on Jupiter.
1636. In Harmonie Universelle, Fr. Marin Mersenne diagrams the construction of reflecting telescopes in configurations similar to the Gregorian and Cassegrain telescopes. Parabolic mirrors are notoriously difficult to grind. Can we say "Hubble Space Telescope"?
1637. Galileo Galilei publishes Dialogues Concerning Two New Sciences. The two sciences are strength of materials, in which he describes the square-cube law, and the physics of motion, in which he confirms De Soto's law and Bradwardine's medieval observations. He even uses Nicole d'Oresme's graphical geometric proof of the Mean Speed Theorem. Without attribution, of course. (The Wikipedia article contains several infelicities.)
Technically, Galileo had been forbidden to publish any new works; but he started writing this while under house arrest in the palace of Archbishop Piccolomini and had arranged for Elsevier to print it in the Netherlands. The same three characters carry on the dialogue here as in his previous work, but curiously, Simplicio is no longer presented as a stubborn and foolish dork. (TOF wonders if this was a sort of peace offering to He Who Must Not Be Compared to a Simpleton.) No one came after Galileo for publishing a new work, so this may simply be an example of the old Renaissance game of official severity coupled with practical leniency.
|Jerry Horrocks spots Venus; forgets to tell|
(*) 24 November under the Julian calendar then in use in England.
|View straight down from the Torre di Asinelli|
8 Jan 1642. Galileo goes off to that great observatory in the sky. Urban's animus pursues him, and will not permit the Archbishop of Florence to bury him in the cathedral as proposed. Geez, can't he let bygonesbe bygones?
29 July 1644. Urban VIII finishes his bucket list and kicks off. Everything is much quieter now.
|I got an idea! Let's replace wars of dynasties with|
wars of nationalism! Then things will be peaceful!
24 Oct 1648. The Treaties of Münster and Osnabrück are signed, ending the rest of the Thirty Years War: between the Empire and France and the Empire and Sweden, resp. But during the peace conference...
All those weeks, all those days, all those last futile hours, they had been fighting at Prague, and went on fighting for nine days longer before they, too, had news of the peace. Then they, too, fired their salvo to the skies, sang their Te Deum and rang their church bells because the war was over. ...
Almost all -- one excepts the King of Sweden -- were actuated rather by fear than by lust of conquest or passion of faith. They wanted peace and they fought for thirty years to be sure of it. They did not learn then, and have not since, that war breeds only war.
-- C.V. Wedgwood, The Thirty Years War
|Tychonic and Copernican systems argue|
on the frontispiece to the New Almagest
while Ptolemy lies prostrate crying
"I will rise again!"
1651. Riccioli publishes his masterwork Almagestum novum. In one section, he presents both major theories -- Copernican and Tychonic -- and gives arguments for and against each one:
- 49 arguments in favor of Copernicanism, with rebuttals to each, and
- 77 arguments against Copernicanism, with rebuttals to each.
“Both sides present good arguments as point and counter-point. Religious arguments play a minor role in the debate; careful, reproducible experiments a major role. To Riccioli, the anti-Copernican arguments carry the greater weight, on the basis of a few key arguments against which the Copernicans have no good response. … Given the available scientific knowledge in 1651, a geo-heliocentric hypothesis clearly had real strength, but Riccioli presents it as merely the “least absurd” available model…”
(Graney, 126 Arguments Concerning the Motion of the Earth 2011.)
|You are here. Riccioli's lunar map.|
Actually, you are not here; but you once were
Unlike Galileo's Dialogue, which was a polemic written for the public, and like Scheiner's Rosa Ursina, Riccioli's New Almagest was a dense, scientific and mathematical tome written for scientists. It remained a standard text into the 18th century. In it, Riccioli also reports the value of g for gravitational acceleration, gives the geography of the moon*, shows that bodies do not fall at the same rate,** et al. He gave detailed descriptions of the experiments so that anyone who wished could duplicate them.
(*) geography of the moon. The New Almagest has the first detailed lunar map, with the sea and crater names that we still use. Riccioli named craters for Copernicus and his followers and for Tycho and Ptolemy and their followers, acknowledging in this offhand manner the collegial and cumulative nature of science.
(**) do not fall at the same rate. If two heavy objects of differing weight are dropped simultaneously from the same height, the heavier one descends more quickly provided it is of equal or greater density. If both bodies are of equal weight, the denser one drops more quickly. Air resistance does matter.
1659. Huygens studies Saturn some more and discovered the true shape of the planet’s rings. Galileo and others with less powerful telescopes had thought the rings were love handles
The 1660s. Nearly 120 years after heliocentrism had been formally proposed, Kepler’s elliptical model has won the contest. The astronomical community has accepted the ellipses with nary a murmur and the Third Law with positive glee. However, the Second Law (the Equal Area law) is rejected as ugly and Kepler’s proof is deficient. But the Rudolphine Tables are just plain easier to use. In the Platonic Renaissance, that carries weight.
There is a long-standing tension between Aristotelians and Platonists over the nature of mathematical physics. The issue is whether something is true simply because the mathematical model is elegant and "works." To the Platonists, the mathematics can be more real than the physics. We see that today in the reliance on complex computer models, in which the model output is sometimes, amazingly enough, called "data." So the Keplerian model was accepted because it was so damn elegant it had to be true and if we keep the faith, sooner or later we'll find the data. But as Einstein once said to Heisenberg, "Theory determines what can be observed."
|A chronology of Chronos.|
1672. Nicolas Mercator develops a correct mathematical derivation of Kepler's Second Law. (Christie, Galileo’s great bluff 2010)
1687. Newton presents his theory of Universal Gravitation. It’s hard for the Late Modern to grasp what a stunning achievement this is. Suddenly, everything makes sense! He does not use calculus to do this. The Principia is carefully structured in correct Aristotelian form, with axioms and deductive logic, to ensure that is true scientia. There is one elegant solution to all the planets, to all the motions! Kepler's laws can be deduced from the principle. Finally, a simple, elegant reason why Kepler’s model ought to be true!
Just one problem; or rather two:
• There is still no @#^$% parallax.
• There is still no *#^%$ Coriolis effect.
Dang! But we can’t let inconvenient facts get in the way of a really kool theory.
Fat lady finally sings!By this time everybody supposes that stellar parallax is simply too small to detect, but there is not yet any empirical evidence that the stars lie at the enormous distances required.
The lack of Coriolis is more troubling. Even though a rotating Earth had been more easily accepted than a revolving Earth, the rotation is still undetected. Newton had described an experiment – dropping a musket ball from a tower – and Hooke had carried it out. But he reported finding no deflection.
Then comes something really unexpected.
|If the earth is moving, the telescope will move during the|
time light from a star travels down the tube. Thus you have
to tilt the tube a little bit.
1728. Building on efforts by Flamsteed, Hooke, and others attempting to detect that old bugaboo, parallax, James Bradley detects stellar aberration in γ-Draconis (Phil. Trans. Royal Soc., 1729).
A similar phenomenon appears when you drive through a snow storm. Even though the snow is falling straight down, it appears to originate at some point forward of your car. This is because as snow falls, your car is moving toward the snow. Similarly, as the starlight falls down the telescope tube, the telescope tube is moving with the earth and the light ray will hit the side of the tube instead of the eyepiece unless the telescope is tilted slightly.
The effect is small, and detectable only with special instruments, but it counts as a proof that the Earth is moving.
Huzzah! Sorta. It may not convince non-specialists, however.
1734. Bradley’s paper is translated into Italian
1744. A "corrected" copy of Galileo's Dialogue is printed in Italy. Not a word is changed, but the term "if" is inserted in various marginal topic headers. This would have been all that was necessary had the original recommendation of the extensor been followed in the Galileo trial.
1758. Copernicanism is removed from the Index. Stellar aberration seems to have been sufficient.
Jun-Sep, 1791. In a series of experiments, Giovanni Guglielmini, a professor of mathematics at the University of Bologna, drops weights from the Torre dei Asinelli in Bologna -- the same tower used earlier by Riccioli and Grimaldi -- and finds an eastward (and southward) deflection. Concerned with windage, he repeats the experiment down the center of the spiral staircase at the Instituto della Scienze and finds a 4 mm Coriolis deflection over a 29 m drop; thus providing direct empirical evidence of the rotation of the Earth. These experiments are later confirmed in Germany (using a mine shaft) and in the United States.
1806. Giuseppi Calandrelli, director of the observatory at the Roman College publishes "Ozzervatione e riflessione sulla paralasse annua dall’alfa della Lira," reporting parallax in α-Lyrae. This provides a simple direct observation of the revolution of the Earth.
|Zeus: I've got a splitting headache!|
Courtier: Uh... Got wimmin on yer mind?
Keplerian heliocentrism had been accepted because it was computationally easier and because it popped out mathematically from Newton’s theory like Athena from the brow of Zeus. But now, finally, 263 years after Copernicus, the dual motions are established by empirical fact. Hot diggity.
1820. Giuseppe Settele, astronomy professor at the Sapienza (now the University of Rome) incorporates these findings into the second volume of his Elementa di Ottica e di Astronomia, and tells his colleague, Benedetto Olivieri (who is then Commissary of the Holy Office) that this provides the demonstration requested by Bellarmino back in 1616. Olivieri agrees, and convinces the Office and Pope Pius VII.
12 Aug 1820. The injunction is lifted in light of the astronomical discoveries made since Galileo's time:
Decree of Approval for the work "Elements of Astronomy" by Giuseppe Settele, in support of the heliocentric systemThe Assessor of the Holy Office has referred the request of Giuseppe Settele, Professor of Optics and Astronomy at La Sapienza University, regarding permission to publish his work Elements of Astronomy in which he espouses the common opinion of the astronomers of our time regarding the earth’s daily and yearly motions, to His Holiness through Divine Providence, Pope Pius VII. Previously, His Holiness had referred this request to the Supreme Sacred Congregation and concurrently to the consideration of the Most Eminent and Most Reverend General Cardinal Inquisitor. His Holiness has decreed that no obstacles exist for those who sustain Copernicus’ affirmation regarding the earth’s movement in the manner in which it is affirmed today, even by Catholic authors. He has, moreover, suggested the insertion of several notations into this work, aimed at demonstrating that the above mentioned affirmation [of Copernicus], as it is has come to be understood, does not present any difficulties; difficulties that existed in times past, prior to the subsequent astronomical observations that have now occurred. [Pope Pius VII] has also recommended that the implementation [of these decisions] be given to the Cardinal Secretary of the Supreme Sacred Congregation and Master of the Sacred Apostolic Palace. He is now appointed the task of bringing to an end any concerns and criticisms regarding the printing of this book, and, at the same time, ensuring that in the future, regarding the publication of such works, permission is sought from the Cardinal Vicar whose signature will not be given without the authorization of the Superior of his Order.
Original Latin source: W. Brandmüller and E.J. Greipl, eds., Copernicus, Galileo, and the Church: The End of the Controversy (1820), Acts of the Holy Office (Florence: Leo Olschki, 1992), pp. 300-301.
That’s a long time to hold out for empirical confirmation.
Aside: The Crucial Role of Galileo.There was none. Every discovery made by Galileo was made by someone else at pretty much the same time. Marius discovered the moons of Jupiter one day later. Scheiner made a detailed study of the sunspots earlier than Galileo. The phases of Venus were noted by Lembo and others. And so on. Even his more valuable work in mechanics duplicated the work of De Soto, Stevins, and others. Matters would have proceeded differently -- certainly with less fuss and feathers -- and some conclusions may have taken longer, or perhaps shorter times to achieve. The thing is, science does not depend upon any single individual. No one is "the father of" any particular theory or practice. As Newton observed, he stood upon the shoulders of giants -- a sentiment expressed by Bernard of Chartres back in the Early Middle Ages! Regarding heliocentrism, Galileo's biggest accomplishment was to get some folks so riled up that the conversation was inhibited for a short time in some quarters.
HISTORY MUST BE CURVED, for there is a horizon in the affairs of mankind. Beyond this horizon, events pass out of historical consciousness and into myth. Accounts are shortened, complexities sloughed off, analogous figures fused, traditions “abraded into anecdotes.” Real people become culture heroes: archetypical beings performing iconic deeds. (Vansina 1985)
In oral societies this horizon lies typically at eighty years; but historical consciousness endures longer in literate societies, and the horizon may fall as far back as three centuries. Arthur, a late 5th cent. war leader, had become by the time of Charlemagne the subject of an elaborate story cycle. Three centuries later, troubadours had done the same to Charlemagne himself. History had slipped over the horizon and become the stuff of legend.
In AD 778, a Basque war party ambushed the Carolingian rear guard (Annales regni francorum). Forty years later, Einhard, a minister of Charlemagne, mentioned “Roland, prefect of the Breton Marches” among those killed (“Hruodlandus Brittannici limitis praefectus,” Vita karoli magni). But by 1098, Roland had become a “paladin” and the central character, the Basques had become Saracens, and a magic horn and tale of treachery had been added (La chanson de Roland). Compare the parallel fate of a Hopi narrative regarding a Navajo ambush (Vansina, pp. 19-20).This suggests that 17th century history has for the bulk of the population already become myth. Jamestown is reduced to “Pocahontas,” and Massachusetts boils down to “the First Thanksgiving.” And the story of how heliocentrism replaced geocentrism has become a Genesis Myth, in which a culture-hero performs iconic deeds that affirm the rightness of Our Modern World-view.
Conclusion: Our ancestors were not fools.In three centuries, the long complex story of how the mobile Earth replaced the stationary Earth dipped below the horizon from History into Legend. Like all good legends, the story of heliocentrism and the culture-hero Galileo is simple and general and geared toward supporting the Rightness of the Modern worldview. But history is always detailed and particular.
The reasons for the stationary Earth were rooted in empirical experience and successful modeling. The dual motion of the Earth is not sensibly evident and was difficult to establish on empirical grounds. Heliocentrism triumphed first of all because Neoplatonic number mysticism had become au courant during the Renaissance, and Platonists equated mathematical elegance with physical evidence.
Resistance to heliocentrism was rooted in the science of the day and religion entered the picture mainly because the Church Fathers had interpreted Scripture in the light of that science. They weren’t about to change until there was solid evidence that the science (and hence the interpretation) was wrong; not in the middle of no honkin' Reformation they weren’t. Thomas Huxley said after investigating the affair that “the Church had the better case.” But Pierre Duhem put it differently. The Copernicans were “right for the wrong reasons.” The Ptolemaics were “wrong for the right reasons.”
Science doesn’t follow a mythic positivist ideal but the plural scientific methods described by Feyerabend: a mixture of empiricism, flights of fancy, intuition, aesthetics, doggedness, and jealousy. Scientific theories are underdetermined. Any finite set of facts can support multiple theories, and for a long time the available facts were equally explained by geostationary or geomobile models.
In the Legend, the conflict was between Science and Religion. But in the History, the conflict was between two groups of scientists, with churchmen lined up on all sides. Copernicanism was supported by humanist literati and opposed by Aristotelian physicists; so it was a mixed bag all around.
Science does not take place in a bubble. International and domestic politics and individual personalities roil the pot as well. The mystery is not why Galileo failed to triumph – he didn’t have good evidence, made enemies of his friends, and stepped into a political minefield. The real mystery is why Kepler, who actually had the correct solution, constantly flew under the radar. A deviant Lutheran working in a Catholic monarchy, he pushed Copernicanism as strongly as Galileo; but no one hassled him over it. Too bad he couldn’t write his way out of a paper bag.
The end. Thank goodness. We now return you to your regularly scheduled blog.
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Bellarmino, Roberto (1615) Letter to Foscarini
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Christie, Thony. (2013) The speed of light, a spin off from longitude research.
Christie, Thony. (2011) A small spot in front of the sun, a small step down the road to heliocentricity. Christie, Thony. But it doesn’t move! June 22, 2011.
Christie, Thony. Extracting the Stopper. June 2, 2010.
Christie, Thony. Galileo’s great bluff. Nov. 12, 2010.
Christie, Thony (2011) Spotting the Spots
Christie, Thony (2011) Questions on spots
Christie, Thony (2013) He didn’t publish and so he perished (historically).
Christie, Thony (2013) Apelles hiding behind the painting
Christie, Thony (2009) Astronomy and Astrology.
Christie, Thony (2013) Refusing to look
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Graney, Christopher M. Tycho was a scientist, not a blunderer. Mar. 6, 2012.
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