Gloria Estefan Was Wrong

 

It's not the rhythm that's going to get you. 

It's the bots. 

I've turned comment moderation on for The TOF Spot because it was overrun with spam comments. I just don't have the time or the energy to be on here daily like Dad was (lol or weekly or...) and I guess since the blog isn't really maintained anymore, the bots are just throwing up trash comments on his more popular posts. I've just spent time deleting them all, and there's still more to go through. 

It's offensive to me personally that they're posting on his death announcement, even though I know it's a bot and not necessarily malicious in that sense. They were also all over that Ptolemaic Smackdown post, which I know was a more popular one of his.

Anyway, I set it up to notify if there's a new comment so ... let's see how terrible this is. If I get a ton of notifications of spambots then ah well. But maybe the closed comments will turn the bots away in search of a recipe blog instead.

Eyeballs on TOF

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As a Matter of Fact

A reader recently asked whether a collection of TOF's non-fiction was planned. The answer is no, but TOF thought that a list of non-fiction might be called for. Herewith:

1. "Universal Range Spaces and Function Space Topologies" (1971) Studia Universitates Babes-Bolyai (Seria Math.-Mech.)

TOF does not dare attempt to explain what it is about, except loosely as follows. A function assigns to each element of a domain space Y a unique element in a range space Z: Z = f(Y) = Y² is an example. A topology defines a "closeness" between two elements in a space. A function space: Z^Y treats all the functions f:Y→Z as elements in a space, with a topology defining closeness among them. TOF proved a couple of theorems about topologies on Z^Y.

In aid of this paper I have migrated two posts from The Auld Blogge onto The TOF Spot for the amusement of the easily amused.

2. "Things Your Mother Never Told You About X-bar and R Charts" (1982?) Transactions of the ASQC Annual Quality Congress.

This was a paper delivered at the annual conference of the American Society for Quality Control, but TOF would have to hunt up the year. An X-bar and R chart is a statistical device for discovering whether a change in a process can be assigned to a particular cause. This paper addressed some common misconceptions about the charts.

A X-bar and R chart compares variation from sample to sample
against the average variation within a sample to determine whether
the long-term variation exceeds the short-term variation. In the
example above, it does; and the process is said to be
"not in statistical control."

3. "What Do Control Charts Really Mean?" (1983). ASQC Qual. Cong. Trans.  pp 448-453

Another ASQC paper, this one ITRC on non-standard control charts, using medians instead of means, extreme values, and so on. 

4. "The Road to Hell" (1984) w/John Bolcar. ASQC Qual. Cong. Trans.  pp 192-196

This was a set of case studies in the interpretation and use of quality control charts, showing that the matter was not always cookbook straighforward. TOF has this reference at second hand since it was cited in one of Juran's Quality Handbooks. Woo-hoo. John was one of my quality engineers.

5. "Garbage Out: The Fine Art of Putting Garbage In" (1986). ASQC Qual. Cong. Trans. p. 149 et seq.

Before you can analyze data you must first collect it, which is easier said than done. This paper, also delivered at an ASQC conference, addressed a number of ways in which you can screw up your sampling. The conceit of the paper was the pretense that you're trying to produce garbage out and these are helpful tips for doing so.

Items #2-5 exist in hard only, if they exist at all, in a file cabinet unlockable by Heisenberg's key. That is, a key whose precise location cannot be pinned down.

6. "An Introduction to Psychohistory" (two parts) Analog (Apr and May 1988)

This was a 2-part article about whether a science of history was possible. Part I was the mathematics of history; Part II was the biology of history. It was reprinted in German in 1991 as an appendix to Heyne Verglag edition of Asimov's Foundation series.

7. "An Astounding 60 Years" Analog (Jan 1990)

TOF was asked by Stan Schmidt, then the editor of Analog to write this article, which is an overview of the first 60 years of the magazine. It's name was Astounding for the first 30 years before John W. Campbell changed it to Analog. Opening paragraph:

It was on or about March 10, 1944, when Counter Intelligence Corps agent Arthur E. Riley knocked on the doors of ASTOUNDING SCIENCE FICTION editor, John Woods Campbell, Jr., and demanded to know what the hell was going on.  The March 1944 issue of ASTOUNDING had just hit the stands with the story, “Deadline,” by Cleve Cartmill.  Although set on an ostensibly alien planet, involving an ostensibly alien war, the story had contained some rather disquieting lines. 

8. "FAT-Eating Logic Bombs and the Vampire Worm," w/ Edward Rietman (Analog, Feb 1993)

Dr. Reitman wrote the original article and TOF was asked to help with the wordsmithing. The whole idea of worms and viruses and the like was pretty new at the time.The opening paragraph:

The Worm from Hell
Shortly after 6:30 PM on 2 November 1988 dæmons struck the Net.  Computers across the country went catatonic.  Berkeley’s Experimental Computing Facility and the Rand Corporation at Santa Monica were among the first to crash.  An hour later, the MIT Artificial Intelligence Lab froze, then Lawrence Livermore and the University of Maryland.  Other nodes toppled like dominoes: Stanford, Princeton, Los Alamos, NASA’s Ames Research Center, the Army Ballistic Research Lab.  By the early morning hours, InterNet was virtually paralyzed.  Only AT&T and Bell Labs were immune. 

The article also made some predictions:

The processor of the future will be filled with the electronic analogs of platelets, antibodies and other such useful critters.  Autonomous programs will run in the background “automatically updating software, diagnosing hardware problems, seeking out information stored in vast data banks or doing routine garbage collection” (Markoff, 1991).  

9. "Pson of Psychohistory" Analog (June 1994)

A very short note in which TOF tried to prognosticate, with variable success. Economic cycles were approximately correct, but individual politicians did not fulfill their assigned roles.

10. "De Revolutione Scientiarum in 'Media Tempestas'" Analog (Jul 2007)

Written in the form of a medieval Question, this article explored the potential for a scientific revolution in the 14th century. It was a companion piece to "Quaestiones super caelo et mundo" which won the Anlab award that year and for which I gave an acceptance speech in Latin, found here.

11. "The Great Ptolemaic Smackdown and Down and Dirty Mud-Wrassle" Analog (Jan/Feb 2013)

This was a summary of the historical transition from the geostationary to the geomobile models of the World, but we had to jettison the diagrams and figures. A more extended, detailed version (with the diagrams and figures) appeared later on this blog. Opening paragraph:

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)

12. "Spanking Bad Data Won't Make Them Behave" Analog (Jul/Aug 2014)

This article was a description of various problems with data. There was to have been a Part II, applying the lessons to Global Warming data, but TOF never got around to writing it. Opening paragraph:

Facts are elusive critters.  Far from being self-demonstrating, they are meaningless without context.  “Theory determines what can be observed,” Einstein once remarked to Heisenberg.  We cannot accumulate answers without first asking a question.  Pierre Duhem put it this way:

“Take two physicists who do not define pressure in the same manner because they do not admit the same theories of mechanics.  One for example accepts the ideas of Lagrange; the other adopts the ideas of Laplace and Poisson.  Submit to these two physicists a law whose statement brings into play the notion of pressure.  They will hear the statement in two different ways.  To compare it with reality, they will make different calculations so that one will find this law verified by facts which, for the other, will contradict it.”  [Emph. added]
– “Some Reflections on the Subject of Experimental Physics” (1894)

So much for the notion that facts alone can settle questions. 

13. "The Autumn of Modern Science" Analog (Apr 2016)

This was a compressed history of the end of the Modern way of doing science, foreshadowed in a few blog posts here and as part of an extended series on the end of modern civilization.  It appeared as a guest editorial in Analog. Opening paragraph:

Thoroughly modern milieu
During the sixteenth century, progress, which had meant a spatial motion, began to mean “improvement.” By 1580, modern had become an adjective and acquired the connotation “new.” This terminological ferment signaled the emergence of new ways of thinking: the Modern Ages.

14. "A Dialogue Concerning the Inner World System" Analog (Oct 2016)

This was a shorter, revised version of a blog post here regarding genetic engineering, written in imitation of Galileo's Dialogo. It appeared as a guest editorial in the magazine. Opening paragraph:

Scene: The Rialto of Venice, Salviati espies Simplicio approaching and greets him.
Salviati: What news on the Rialto, good Simpicio?
Simplicio: Well-a-day, my friend. Work progresses on our engineerings genetical. Soon we shall be "the sort of people we should be."

Underdetermination

Natalie Wolchover, Quanta Magazine

One hears much that scientific theories are underdetermined; that through any finite collection of facts, one may draws countless explanatory theories. The existence of at least four or five theories of quantum mechanics to explain the same body of facts is an illustration, even if one of them is more popular than the others.¹ ² The Copenhagen Interpretation insists that all potencies exist until the particle is actualized by measurement. The equations don't tell us how a particle’s properties "solidify" at that moment of measurement, or "how reality picks which form to take. But the calculations work."

Although in matters of religion the existence of multiple interpretations is said to prove that there is no "there" there, it does not do so in matters of Science!™ because Invisible Sky Fairies! It is simply in the nature of theories that there can always be more than one for any given set of data. Recall how, at the dawn of the modern age there were multiple theories explaining the motions of the heavens, with the Ptolemaic theory being the most popular, the "consensus science." The calculations worked, but they did not tell us how the planets moved as they did.

But "the quanta are a hopeless mess" and it is useful to have a more homey example of underdetermination. Detective fiction is good at this: maintaining multiple theories of whodunnit until the end, when a new fact or a new arrangement of the facts collapses the potencies into an actual. The new fact may be the discovery of stellar aberration or the Afshar Experiment.

But here is an example of how a fact may support multiple theories:

Matt Briggs, the Statistician to the Stars, recently noted a kerfuffle in the rarefied world of chess.

Chess Grandmaster Nigel Short caused a stink, reaching oooo-weee! but not quite burn-him! levels, when he said that men and women are different and that men are better at chess than women.

Female chess player Amanda Ross said in response that, it is “incredibly damaging when someone so respected basically endorses sexism”. Sexism is when a disparity of any kind exists between males and females.

Let's call these the Short Theory and the Ross Theory.
So let us appeal to the Facts! In a list of living Grandmasters, there are:

• 1413 men 
• 33 women.

This fact supports Short's theory that men are better at chess.

It also supports Ross's theory that sexism in chess suppresses women's achievement.

This is why proponents of a theory are seldom swayed by the facts. Facts alone have no swaying power, since they will (and must) be interpreted in the light of some theory.


Notes:
1. Further confused by the fact that the mathematical formalism common to them all is also referred to broadly as "quantum theory." But "quantum theory" as such is not a theory. 
2. For the record, four that come trippingly to mind are:

a) Copenhagen (Bohr, Heisenberg), which reifies Aristotelian potencies until measurement collapses reality onto one of them.
b) Standing Wave (deBroglie, Bohm), in which the particle rides on the wave.
c) Many Worlds (Wheeler) in which all potencies are actualized, but in different worlds.
d) Transactional (Cramer) in which the wave travels backward as well as forward in time, thus reifying final cause.

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First Way, Part II: Two Lemmas Make Lemma-aid

TOF's Dilemma

We are now ready to prove two lemmas regarding motion,  hence... dilemma. ROFL. Never mind. We interrupt this pun to stay on focus. Besides, there are a couple of initial propositions.

Those who have been following these maunderings would be well-advised to read

• Background and 
• Part I 

lest they lose themselves in the woods. First, we have to get a word out of our way.

Disaster at Lunacon!

TOF was "special guest" at Lunacon this past weekend, and very special he was. He got to wear a ribbon like unto a prize steer at the stock show and had melons placed under his arms. In return, he sat upon certain Panels, picked a Winner at the Art Show, and started a presentation on THE GREAT PTOLEMAIC SMACKDOWN. 

TOF at Lunacon

TOF is "special guest" at Lunacon this weekend.  If you're near the RyeTown Hilton, here is his schedule AFAIK

1. Fri 4:00 PM     Character Building     Bartell     Your clever plot twist or interesting theme will mean nothing if readers don't care about your characters. The panelists will discuss techniques to use to make sure your characters are memorable and that the story is about them.
2. Fri 10:00 PM  Rules! Rules????? There are no Rules!     William Odelle     When writing fiction, if it works, it works. Our panel debates whether authors need to know "rules" that they can then break if they are good enough, or if this only constrains creativity.
3. Sat 11:30 AM     Reading: Michael Flynn     Elijah Budd 
4. Sat 2:00 PM     Alternate History That Isn't About War     William Odelle   Can't we imagine alternate history about something other than the outcomes of battles. Think of how history might have changed if certain IDEAS had formed differently or come at different times.
5. Sat 3:00 PM     Magic and Religion     Westchester Ballroom A2   How do Magic and Religion intertwine?
6. Sat 4:00 PM     Autographing: Michael Flynn     Westchester Assembly       
7. Sun 1:00 PM  The Great Ptolemaic Smackdown     Westchester Ballroom B     How the heliocentric world replaced the geocentric one against all evidence and common sense.

America's Next Top Model -- Part II

PREVIOUSLY, WE DISCUSSED the emergence during and after WW2 of model-building as a means for dealing with organized complexity, a distinction, first made in 1948 by Dr. Warren Weaver:

1. Organized simplicity. Systems with few elements. Analyzed mathematically.
2. Disorganized complexity. Systems with many elements acting "randomly." Analyzed statistically.
3. Organized complexity. Systems with many interconnected elements. Analyzed with operations research/model-building methods.

George Box said that "all models are wrong" because of the uncertainties to which models are subject. Honest modelers are obligated to assess these uncertainties and to inform their clients of them. Alas, too few do, and models are presented, understood, and press-released as being more certain than they actually are.

Joe Martino tells TOF that "One of the most horrible examples I ever encountered was the use of a Cobb-Douglas Production Function to predict the effectiveness of bombing the Ho Chi Minh trail. When I first saw the model it fairly screamed 'wrong!' But the people who put it together saw nothing wrong with it."

And yet, these things have so many pretty equations they seem like they damn well ought to work. And they do, in some cases. Kingsbury Bearings has a model for hydraulic bearings that works well in predicting the performance of new bearing designs.* So what's the problem?  Operationally, what is the difference between a model that is "useful" and one that is "true"?

(*) hydraulic bearings. TOF digresses. At the entrance to the Kingsbury plant is a placard honoring the Kingsbury Bearing installed in Holtville #5 in 1912. TOF inquired of his hosts in the 1980s when he spent some time with them: "How long did it last?" "We don't know yet," was the response. "It's still running." As of 2008, Wikipedia tells us, it was still running with an estimated TTF of 1300 years. That's craftsmanship! It's also a system whose elements and interactions are pretty well understood.

Slouching Toward Philadelphia

TOF was tied up for most of Philcon. Having committed himself to attending a symposium in Greenwich Village on Saturday, there was no point hustling down to Philly Town for Friday, especially inasmuch as TOF had not been scheduled for diddly squat at the con except for an autographing on Saturday morning when no one would be awake to request one, and a panel on Sunday morning, which he decided to attend just to see if anyone was awake. 

They were.

A few.

Retroview: The Wreck of "The River of Stars"

Apologia pro blogpost sua: An earlier, incomplete draft of this may have posted temporarily before the gods of BlogSpot obliterated it by freezing up the Insert Picture tool.  This is a re-draft from scratch. 

+ + +

Ain't TOF cute?

Taking a break from the heavy Ptolemaic lifting, TOF has decided to ruminate on his "critically-praised" but commercially orphaned novel, The Wreck of "The River of Stars," the title of which is the despair of orthographers everywhere.  To do so, he will abandon his cute affectation of referring to himself in the third person.  This does not mean he will cease being cute, however.  

The Wreck, if we may call it by its nicktitle, was called by one reviewer "the best hard-SF tragic novel of character yet written," adding "though this is an uncrowded niche."  Uncrowded, indeed.  Run out and buy a copy.  I'll wait.  

The Great Ptolemaic Smackdown: TABLE OF CONTENTS

1. The Great Ptolemaic Smackdown

2. The Great Ptolemaic Smackdown: Down for the Count

3. The Great Ptolemaic Smackdown:
The Great Galileo-Scheiner Flame War of 1611-13

4. The Great Ptolemaic Smackdown:
The Down 'n Dirty Mud Wrassle

5. The Great Ptolemaic Smackdown: Here's Mud in Yer Eye

6. The Great Ptolemaic Smackdown: Comet Chameleon

7. The Great Ptolemaic Smackdown: Time and Tides Wait Not

8. The Great Ptolemaic Smackdown: Trial and Error

9. The Great Ptolemaic Smackdown: From Plausible to Proven   

9. The Great Ptolemaic Smackdown: From Plausible to Proven

Previously: Part 8, Trial and Error

From Plausible to Proven

 

The great dishonesty of Galileo’s Dialogue was to present a contest between the Copernican and Ptolemaic models.  By that time, both had been smacked down and the real contest was between the Tychonic/Ursine models and Kepler’s model, with the Ursine model being “ahead on points.”  Galileo did not mention either one. He regarded the Tychonic/Ursine models as unaesthetic and klunky.  He seems to have regarded Kepler's model, which came annexed to a physics in which the Sun put out a mysterious force that chivvied the planets about, as occultism.  Besides, he was committed to perfect Platonic circles, and Kepler had ellipticated them.  Boo. 

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.

8. The Great Ptolemaic Smackdown: Trial and Error

Previously on the Smackdown

Galileo has just published his Magnum Opus. 


Several things have combined to create the perfect sh*tstorm.

• The best minds from the time of Aristotle to the then-present had held the earth is stationary for sound empirical reasons.  
• Because it was "settled science," the early Church Fathers had taken it for granted in their reading of the Scriptures, and so Patristic writings are full of rhetorical invocations of the stationary earth.  
• While there is no dogmatic bar to reinterpreting scripture when some literal reading was known to be wrong, no one is about to do so for a merely plausible hypothesis.  Hence, heliocentrism must be proved beyond doubt.  
• The Pope thinks that scientific theories can never be proved with certainty.  They are either useful as instruments for prediction or not.  (This is called instrumentalism.)  In particular, he does not think that the motion of the Earth can ever be proved contrary to plain experience.  In this, he is way ahead of Popper.  
• The Pope had been an old friend of Galileo and had helped him out on several occasions.   
• Galileo has taken the Pope's instrumentalist argument and placed it in the mouth of Simplicio, in the Conclusion, apparently assuming that having done so and having his characters nod in agreement to it, he has touched the right bases in satisfying the requirements.  
• But when read after the entire rest of the Dialogue, it comes across as a fatuous objection made by a simpleton and the nodding agreement a patronizing pat on "the Simpleton's" head.  
• Prince Cesi, who had the street smarts (and connections and lived in Rome) could have headed off the collision, but Cesi died before the manuscript was ready for publication.  
• The plague has shut down travel and the post, so Galileo cannot either send or take the ms. to Rome and wants to publish it in Florence.  
• Galileo has used Medici political muscle to force an imprimatur from Riccardi (or, more precisely, forced Riccardi to pass the buck to Egidi, the Florentine Inquisitor.)  

• Father Riccardi (aka Fr. Monster), the master of the palace, has read only the Preface before passing the buck.  He tries to brief the Inquisitor on the Pope's concerns, but the Inquisitor does not have the Preface and Conclusion, only the body of the manuscript.  It is not clear whether anyone -- Riccardi, Egidi, Stefani (Galileo's hand-picked reviewer in Florence), or the Grand Duke's secular book reviewers -- has read the Conclusion in conjunction with the Dialogue.  
• Given the international situation -- and a fistfight in his own consistory between Bourbon and Hapsburg cardinals! -- Urban has no time or patience for an argument on astronomical mathematics.  But an ingrate must be shown his place.  

Once the book comes out, someone "helpfully" points out to Urban the apparent slap in the face contained in the Conclusion.  In the Renaissance lexicon, there is little that is worse than ingratitude.  Friendship betrayed turns rancid hate.  The problem is that Galileo is vain and impatient of opposition while Urban is... exactly the same kind of personality.

The Sideshow

These posts started out to be a chronology of how the geostationary models gave way to a geomobile model; but TOF has gotten sucked into the black hole of Galileo.  Suffice it to say that the Dialogue did nothing to establish geomobility as fact.  The arguments were plausible; though the main argument -- the tides -- was simply wrong.  And the main objection to Copernicanism -- the lack of stellar parallax -- was dismissed by adding an epicycle, that is, a second unproven hypothesis: that the stars were much farther away than currently believed.  (That would indeed account for the lack of visible parallax; but there were sound observational reason for supposing the stars to be closer: the visible discs they showed to Tycho's eyes and Galileo's telescopes.  They couldn't be too far off and show such discs without being absurdly enormous, bigger than the solar system.)  Galileo proposed looking for parallax in close optical doubles; but he himself had done so with Mizar and failed to find any angular change.  Theoretically, this falsified his theory, but the fact (much later) turned out to be that Mizar is a binary star, not an optical double and really would not have shown parallax due to the Earth's motion.

So let's finish the trial briskly and get back on track.  

7. The Great Ptolemaic Smackdown: Time and Tides Wait Not

Previously on the Smackdown

The faces of Venus

Previous episode: Comet Chameleon

The discovery of the phases of Venus by a variety of telescopists in the early 1610s has put paid to the long, happy consensus science of the Ptolemaic model, which now languishes on the ash-heap of history.  The Aristotelians are gleeful, since Ptolemaic astronomy was at serious odds with Aristotelian physics.  (Much like today's quantum mechanics is at odds with relativity.)  However, they should hold their gobs, since several bits of Aristotelian Physics have also come under telescopic doubt: the Moon has mountains, Jupiter has moons, the Sun gots freckles, and comets have most unhappy orbits. 

None of this proves the Earth is mobile or that the Sun is at the center of the World.  The stationary Earth remains unimpeached and her alleged dual motions are falsified in the Popperian sense by a) a lack of visible parallax among the fixed stars (which falsifies the Earth's revolution) and b) a lack of discernible Coriolis effects (which falsifies the Earth's rotation). There are other counterarguments, as well, which await the development of such concepts as inertia. TOF would discuss inertia, but it's hard to get started. 

Meanwhile, Galileo has been suckered by the Pigeon League into dabbling in Scriptural interpretation, never a good idea for an amateur during a Protestant Revolution.  He's been cleared of suspicion of heresy in a confidential investigation, but in the process Copernicanism has attracted the notice of the Authorities -- who are mostly lawyers and politicians.  Galileo tried to re-interpret Scripture because of his commitment to Copernicanism-as-physically-real and -- much as people react to a mass shooting by concern over guns (rather than, say, lunatics) -- the Authorities react to this free-lance exegesis by a concern over heliocentrism.

A decree of the Index had removed Copernicus' book from circulation for a few years pending a couple of corrections to statements that seem to assert the physical reality of the model.  Galileo has been cautioned not to hold or teach the theory other than as a mathematical model.  However, the late Cardinal Bellarmino had written that if a demonstration could be shown, there would be little problem in clearing up the  Scriptural issues. The Church has never insisted on strict literalism.  But while the Church, holding that Truth is One, would have no problem reading a scripture non-literally if the literal reading could be certainly demonstrated false, they are not about to do so for the sake of a plausible mathematical hypothesis.  Given the history of science, this would hold exegesis hostage to phlogiston, or any other scientific fashion. 

So all Galileo needs to do now is present empirical evidence that the Earth has a dual motion.  Piece of cake.

Or is it? 

6. The Great Ptolemaic Smackdown: Comet Chameleon

Previously on the Smackdown...

1. Galileo's enemies have managed to suck him into a theological discussion, never a good idea for a private individual during a Protestant Revolution.  The lawyers and politicians who run things have almost no understanding of and little interest in natural science. They see it only as a hairy nuisance getting some folks riled up and they want to make it go away.  Even the Lynceans are mostly naturalists and lack deep understanding of astronomy.
2. Galileo has been asked politely to prove that the Earth really does move before he demands that the Church reinterpret the Scriptures.  But the Tuscan mathematician is an irascible and impatient sort.  He sees things so clearly that the demand for proof seems like pig-headedness and, alas, he starts to see proofs where they are not.  
3. The upshot is that in 1616 Copernicus' book has been withdrawn from publication -- the third edition has just come out -- to await corrections.  That it was not banned outright is evidence that the authorities have no problem with heliocentrism per se, only with the assertion that it is physical fact (and therefore etc.)  Two other books that delved into Scripture in the name of Copernicanism -- those by Foscarini and by de Zuñiga -- have been banned, indicating what really matters to the Holy Office. 
4. Galileo is okay with this, because he believes that before long he will have the physical proofs Bellarmino wants.  Then he will Write a Book.  

We must not suppose that Galileo brought everything on himself by his arrogant personality, though that surely isn't helping.  (Lots of people are talking up geomobility without raising a stink.   Kepler, for example, has been appointed Imperial Mathematician by the Catholic Emperor.*)  Galileo has been systematically hounded by a band of Aristotelian enemies led by Ludovico delle Colombe, who have more or less compelled him to answer in theological terms.  He genuinely frets that if they keep it up they will badger his beloved Church into taking a theological stance on a matter of empirical fact. 

(*) Imperial Mathematician.  At this point, Kepler has been given permission to move to Linz and work on the Rudolphine Tables, a practical manual for applying his weird elliptical astronomical model. 

But neither should we suppose that the Church authorities are "out to get" Galileo due to some deep-seated science-hating hostility of science haters.  Everyone thinks they are on the side of science, and none of them -- not even Galileo -- think of science in the way we do today.  The authorities are rather well-disposed toward Galileo, especially those like Bellarmino, the Barberinis, del Monte, and others of "the Tuscan clan" within the Curia, who cut him every break they can.  Bellarmino gave him a heads up on the decree of 1616 so that he would not be taken by surprise and publicly embarrassed, and had no trouble providing Galileo with a certificate saying that Galileo himself had not been accused of anything.  Once the corrections to Copernicus' book are made, he is welcome to use and discuss it as a mathematical model.  It's only that until he has proof, he cannot say it is physical fact.   

Although Bellarmino showed an understanding of what we today recognize as scientific method, we can't say that he issued the decree out of tenderness for the purity of scientific methodology.  Many scientific theories have been proclaimed -- and accepted -- in advance of their proofs -- Maxwell, Darwin, Einstein, etc.  But it has not yet quite sunk into the 17th cent. Zeitgeist that the heavens are a physical place in which physical discoveries can be made.  Though it is beginning to change, astronomical theory is still instrumentalist: a specialized branch of mathematics whose purpose is to devise models that accurately predict heavenly events.  In fact, the heavenly bodies are so distant and so devoid of sensible properties -- only location, speed, brightness, diameter can be seen -- that it is unlikely that any physical theory regarding them can ever finally be proven.*

(*) finally proven.  In the Late Modern Age, we have extended that to all of science.  Nothing is ever proven.  From time to time things are falsified.  Had Galileo known of Popper, he would have despaired. 

As of 1617, Galileo has returned to Florence to work on his Big Book; Kepler is in Linz developing the Rudolphine Tables; Scheiner is working on his own magnum opus on the sunspots; Simon Marius has discovered the Andromeda Nebula -- no one will know it's a galaxy until much later.  But TOF's Astute Reader will note that no progress has yet been made on establishing the dual motions of the Earth.  If we assume the Earth moves, we can make accurate predictions of the heavens; but if we assume she does not, the Tychonic model also makes accurate predictions.  The Copernican and Tychonic models are mathematically equivalent, differing only in the origin of their reference frames.  To decide which reference frame to privilege will require physics, not math.

Wussup?

In 1617:

• René Descartes (21) has just graduated college and will shortly enlist in the army.  He is about to meet... 
  
• Isaac Beeckman (29), a student of Willebrord Snel, who will anticipate much of Galileo's mechanics.
• Marin Mersenne (29), newly ordained, is teaching theology and philosophy at Nevers and will set up a correspondence network among the scientists of Europe that will include Galileo, Descartes, Beeckman, Gassendi, and Peiresc.  He will help translate Galileo's works into French.
• Pierre Gassendi (25) is about to be ordained.  
• Nicolas-Claude Fabri de Peiresc (39) has discovered the Orion Nebula. 
• Joseph Gaultier de la Vallette (55) had with Peiresc observed the moons of Jupiter back in 1610, shortly after Galileo and Marius, and had been the second to see the Orion Nebula.
• Old Simon Stevin (69) had in 1586 dropped two balls of differing weights from the church tower in Delft, proving that they fell at the same rate.  He also discovered "Pascal's" Law. As science advisor to Maurice of Nassau, he may well have been present when Lippershey demonstrated his telescope in 1608. 
• Nicholas Zucchi (30), a friend of Kepler, has invented a reflecting telescope in 1616 using a borrowed parabolic mirror and some lenses.  The primitive design did not provide a way to keep the head of the user from intercepting most of the rays needed to form the focal image, but he will use it to discover the belts of Jupiter in 1630 and examine the spots on the planet Mars ten years later. At the urging of another Jesuit scientist, Paul Guldin, Zucchi will present a reflecting telescope to an enthusiastic Kepler.

All of these save Gaultier and Beeckman have Lunar craters named for them, as do Clavius, Tycho, Galileo, Kepler, Marius, Fabricius, Scheiner, and Harriott.  All those things that seemed so important 400 years ago, all the disputes over who was right and who was wrong and who was first are vanished now into the democracy of the dead and the landscape of the moon. 

Then came...

5. The Great Ptolemaic Smackdown: Here's Mud in Yer Eye

Previously on the Smackdown...

1. For sound empirical reasons the consensus science of 1400 years had been that the Earth is stationary at the bottom of the world and the Church Fathers anciently interpreted Scripture in the light of this settled science.
2. In the early 1600s, a series of telescopic discoveries made nearly simultaneously by Harriot, the Fabricii, Marius, Galileo, Scheiner, Lembo, et al., had broken Ptolemaic astronomy beyond repair.  But falsifying Ptolemy does not affirm Copernicus.  The Tychonic model seemed the best alternative at the time.  After all, if a geomobile theory were factual, it would require an entirely new physics, and no one had one handy.
3. One discovery -- the sunspots -- triggered a flamewar of epic proportions between Fr. Christoph Scheiner SJ, a mathematician in Ingolstadt, and Galileo Galilei, a mathematician-courtier of the Florentine Grand Duke. This will have Dire Consequences later. 
4. Die-hard Aristotelian Lodovico delle Colombe attacks the new discoveries in a paper, some philosophers refuse to look through a telescope, some look but see nothing.(*)  Galileo ignores or mocks them.  Then della Colombe's "Liga" engineers a series of attacks, first by Lorini, then more scandalously by Caccini, finally by a formal complaint filed by Lorini with the Holy Office.  The Office dismisses the complaint without prejudice.  
   
   (*) see nothing.  With good reason.  The first telescopes did not produce great images. 

 Curses, foiled again.

In today's episode....

4. The Great Ptolemaic Smackdown: The Down 'n Dirty Mud Wrassle

Previously on the Smackdown...

1. We have seen that there were sound empirical reasons for accepting the consensus science of a stationary earth, in particular the lack of stellar parallax and of Coriolis effects.  
2. In particular, the Church Fathers had interpreted Scripture in the light of this settled science, since like everyone else they assumed the scientists had gotten it right.  This consensus has stood for 1400 years. 
3. In the early 1600s, a series of telescopic discoveries had shaken Aristotelian cosmology and one (the phases of Venus) had broken Ptolemaic astronomy beyond repair.  These discoveries were being made nearly simultaneously by mathematicians all over Europe: Harriot, Fabricius pere et fils, de Peiresc, Marius, Galileo, Scheiner, Lembo, and others.
4. Since the earth was "clearly" stationary, most astronomers shifted to the Tychonic or Ursine models.   A few -- mostly humanists rather than scientists -- rallied around the Copernican model.  Kepler's elliptical model for some reason flew below the radar. 
5. One discovery -- the sunspots -- resulted in a flamewar of epic proportions between Fr. Christoph Scheiner, a mathematician in Ingolstadt, and Galileo Galilei, a mathematician-courtier of the Florentine Grand Duke. 

It is 1613, and Galileo has published his Letters on Sunspots, after the censors have removed all of his appeals to Scripture.  (They did not object to his straight-up endorsement of Copernicanism.)  Meanwhile, Galileo's enemies are preparing an attack.  Several men of a severely Peripatetic persuasion have formed a "league" (as they have called themselves) under Ludovico delle Colombe.  Learning of this, Galileo calls them the "Pigeon League" (since colomb means "dove").  Ludovico, he says, never opens his mouth without saying something stupid.  Galileo's love of a witty put-down could get him in trouble some day.

"But my most holy intention, how clearly it would appear if some power would bring to light
the slanders, frauds, stratagems, and trickeries that were used eighteen years ago in Rome in
order to deceive the authorities!"  

-- Letter: Galileo to Peiresc (22 Feb 1635)

3. The Great Ptolemaic Smackdown: The Great Galileo-Scheiner Flame War of 1611-13

Previously on the Smackdown...

...we have seen that the immobility of the earth was 'settled science' and 'the consensus' for excellent empirical reasons, while geomobile theories had been falsified on several grounds, most decisively on the lack of stellar parallax (which falsified the earth's revolution) and the lack of Coriolis effects (which falsified the earth's rotation).  We now know that these falsifications (like all falsifications) have been falsified by what we might call the Duhem Effect.   

Popperian falsification is known in logic as modus tollens.  

M: If A, then Y. 
m: But not-Y
/.: not-A

But there is never just one A, so what we always have is:

M: If A and B, then Y.
m: But not-Y
/.: Either not-A or not-B 

Thus, it is never evident on the face of it which of the prior assumptions -- and there will be more than two! -- has been falsified when Y fails of observation.  The problem is, it's hard to know what unspoken assumptions you are assuming.  The lack of stellar parallax was thought to falsify A (Earth goes round the sun) but it actually falsified B (the stars are millions of miles away).  In fact, they are billions of miles away and the parallax is too small for eyesight to detect even with a 20x telescope. The stellar distance was believed to be fact, based on the brightness and diameter of stellar disks.  But it turned out (in the 19th cent.!) that the "disks" were optical illusions caused by aberration and the stars differed in intrinsic brightness. But we are still here in the 17th century.

In the second episode, we saw a slew of new telescopic discoveries during 1610-1611; viz., the mountains on the moon, the Medicean stars, and (more decisively) the phases of Venus.  Now the first two do not demonstrate geomobility, not do they undermine geostationarity.  The first indicates that the moon is not incorruptible.  But this is agreed to by theology, and it undermines only Aristotelian physics.  The second indicates that some heavenly bodies -- Cosmo, Franco, Carlo, and Lonzo -- circle Jupiter and not the Earth.  This bothers Aristotelian physicists, but not Tychonic astronomers.  Only the phases of Venus KOs Old Man Ptolemy.

But eliminating Ptolemy does not prove Copernicus any more than eliminating Darwin would prove ID.  There may be [and were!] other alternatives.  When Ptolemy was ptossed, astronomers flocked... to the Tychonic and Ursine systems -- because none of the telescopic observations have so far established the motions of the Earth.  Of the seven models of the world that were in play at the beginning of the century, four are still in the running, although the kumbersome Kopernican was fading fast:

1. Heraclidean 
2. Ptolemaic
3. Copernican
4. Gilbertian
5. Tychonic
6. Ursine
7. Keplerian

It was a new, modern age.  Everything was changing.  Who knew what might happen next?

The Sun Gots Freckles!

2. The Great Ptolemaic Smackdown: Down for the Count

In the Previous Post

found here, we saw that the geocentric/geostationary model of the world was not only not unreasonable, but was the best fit for the empirical data that was then available.  Inter alia, you could see the stars and planets moving around the earth!

Oresme subverted that evidence in 1377 in his Livre du ciel et du monde, with an argument from relativity of inertial reference frames.  Whether the Earth were turning and the heavens stood still or vice versa, everything would look the same.  He also proposed "common motion" to counter the Argument of the Winds.  None of these arguments were conclusive and Oresme lacked the sort of instrumentation that might have provided him with better information or the conceptual lumber (inertia, forces, ...) that would have let him frame the issue.  

The main obstacle to the revolution of the Earth was the lack of stellar parallax.  Copernicus (among others) proposed that the stars were really far away and thus the parallax would be too small to see with the naked eye.  But this was saving one unproven hypothesis by throwing in a second unproven hypothesis.  The stars could not possibly be as far away as Copernicanism required because then, given their visible disks, elementary geometry required the stars to be of such enormous size as to dwarf the solar system.  Tycho (among others*) thought this absurd, as it would mean an entire class of new entities.  The Copernicans answered by saying "Goddidit!"  “Who cares how big the stars are?” wrote Christoph Rothmann, since an infinite Creator God is far bigger still.

(*) among others.  Little in the history of science is due to Just One Person.  There is no
"Father of..." this or that.  Those who get credit are typically lucky, more astute in PR, or
standing on someone's shoulders.  The best of them, like Newton, will tell you so. 

Notice, en passant, that it was the Earth being stationary that mattered, not it's being 'in the center.'  The ancients and [especially] the medievals, saw the Earth as being in the bottom of the world, the most ignoble place.  That's why Copernicanism was supported by humanists but opposed by physicists.  It elevated Earth (and humans) to a higher position in the universe.  

1. The Magnificent Seven.