Signing off
Was the Galileo Affair inevitable?
By Jason Rhode
(Taken from a paper written for di Poppa’s Modern European Philosophy Grad Course. I have edited it substantially to make it readable to my readers on Facebook, and to add my own personal observations.)
I wish to examine Galileo Galilei's 1615 Letter to the Grand Duchess Christina of Tuscany (L) through the lens of game theory. For brevity’s sake I will assume that my audience has some knowledge of the conflict between the players Galileo (G) and the Catholic Church (CC) which began with Starry Messenger in 1610.
Game theory has a mixed lineage as far as accuracy in representing human affairs. Some days, I consider it in the same light I do the Chicago School of Economics: a neat model employed by academics funded by corporate/defense think tanks that seems cool in some aspects but fatally flawed as far as mimicking reality.
Other days, I think it’s the best thing ever. In the paper that I wrote for di Poppa, I took the “Best Thing Ever” tack.
Because to say that game theory is fatally flawed because it does not fully and accurately represent the mundane world is like faulting Mercator’s map for not being correct about the continents or as wet as the oceans; it’d be like eating a Chinese restaurant menu and then complaining it doesn’t taste like General Tso’s chicken.
Not as a representational model, but as a explanatory model, does game theory have real and impressive (to me at least) value. Then again, I haven’t gone deep enough into it to have even a novice’s expertise, so take my opinions with a grain of salt.
No, not album by the Roots. Well, some of us may not be familiar with game theory. Here’s what Wikipedia says:
Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others.
A game consists of a set of players, a set of moves (or strategies) available to those players, and a specification of payoffs for each combination of strategies.Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games.
In other words … mathematics and science take apart games to see how conflicts work, and what are the best strategies in different kinds of conflicts. They then try to translate these findings to the real world.
In game theory, there are “cooperative” aka “ non-zero-sum” games, where both players can benefit – I give you a bushel of wheat for a bucket of fish. That’s a non-zero game. Sex is a non-zero game. In non-zero games, we can have win-win and lose-lose situations. The existence of non-zero-sum situations is what makes all economics and maybe all of human interaction possible, if you follow game theory down the trail that way. When you think non-zero/cooperative games, think “economics” or “peace treaty.”
In “non-cooperative” aka “zero-sum” games, there has to be a winner and a loser. Think of a chess game: every victory for your side is a loss for the other side: taking pieces captive, securing territory, and so on. Zero-sum games are to the death, or to the certain disadvantage of both parties. Arm wrestling is a zero-sum game: there has to be a winner, and a loser. When you think of zero-sum games, think of “arm-wrestling,” “chess,” or “war.”
Back to a history of game theory. Well: After the Second World War, the cheery prospects of incipient nuclear holocaust pushed the Pentagon to cook up the RAND thinktank and staff it with McNamara-looking grey flannel drone-men, probably looted or borrowed at any rate from IBM, where they were cloned in tanks and taught Mainstream Protestantism through speaker tubes, as in Brave New World.
Just kidding. What they did was get the smartest people in America in one room and let ‘em come up with all kinds of wild shit. This was the era of the Brain Trust; the professors domestic and foreign had gathered to create a false sun in Los Alamos.
The Intellectuals. The Scientists. The men in white lab coats.
They had given us the bomb and they might give us much else. The RAND guys used wargames and computers to completely rethink strategies, tactics and systems for the Cold War. Picture a room with guys with short shirtsleeves and slide rules, the sort of get-together necessary before the big computers that scared the hell out of us in War Games were possible. Here are pictures of the Rand boys. This is what alpha-nerds did in the quiet years between World War II and Wikipedia:
The social scientists at RAND, the great far-visioned planners of the mid-20th century (this was also the age of Robert Moses and bulldozing neighborhoods to make way for rational highways) were encouraged to create mathematical models that often bore only a faint resemblance to reality. They were needed to avoid the End of All Things under a mushroom cloud. New American citizen Johnny Von Neumann's game theory required endlessly sophisticated math, and was mysterious but mickle in the projections of the postwar American order.
In 1950, two guys at RAND, Flood and Dresher, came up with the most famous game in game theory, the first game you learn about in any game theory book or class. It is called “The Prisoner’s Dilemma”:
Two suspects are arrested by the police.
The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal.
If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence.
If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge.
If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
As Wikipedia points out, in the iterated prisoner's dilemma, the game is played repeatedly. Each player has an opportunity to punish the other player for previous non-cooperative play, i.e., for stabbing him in the back the turn before.
This chart shows the various outcomes for all games possible in a single play of The Prisoner’s Dilemma:
Write your own moral from the above. It might be something like selfishness is not the solution or why is there still war if it’s so destructive for everyone involved? Here is a possible explanation or even something like Snitches don’t always get stitches. Use your imagination.
Here’s a wonderful explanation of Game Theory written by Brian Shader of Everything2:
It is important to understand that game theory applies beyond the bounds of what one would usually consider "games". Certainly game theory has something to say on games like Chess and Go, but it applies equally well to any system where parties are in potential competition. I say potential because game theory also handles ideas like the emergence of co-operation! You will perhaps now be getting a feeling for how broadly game theory is actually spread.
An example of a 'game theory' emerging in a situation which is certainly not considered a game by most affected would be in the recent firemen's strike here in the UK. This is certainly a game according to our earlier definition, having competing parties - firemen and the government - and a number of end results. Yet it is of the utmost seriousness! Note also that it needn't be a zero-sum 'game'; had it been resolved earlier, both parties might have come out of it better off. As it is, both parties will probably lose public favour.
It is these non-zero-sum games that most interested the great John Nash, subject of the film A Beautiful Mind.
There's a fair amount about that great hero of game theory under his node, but within the topic of this one I'd like to point out just how far-reaching his ideas were.
In nature, non-zero-sum games are just as common as zero-sum ones -- unlike humanly constructed games, where we would usually consider it quite strange for both sides to lose! His work on Nash equilibrium had huge implications for an array of topics. To borrow a quote from that node, Nash equilibrium was described as "the most important idea in noncooperative game theory... whether analyzing election strategies, or causes of war."
That was the first point I wanted to make. Game theory is everywhere. It makes enough sweeping assumptions to satisfy any physicist, and yet it does have applications in the real world and provides us with much interesting mathematics to study.
Read David Levy on human aggression and social order seen through the game theory lens:
In his Leviathan, Hobbes contended that in a free “state of nature” unrestrained by fear of retaliation, each man's self-interest would unleash his “natural passions” in violence. Freedom and self-interest seemed to condemn man's life to being “solitary, poore, nasty, brutish and short.”
In game theory language, Hobbes attacked a society of individual freedom with the “prisoner's paradox: that state of affairs in which an individual's maximizing of his own utility does not seem to lead to maximizing results for the group.”
In effect, we need the fear of Big Brother, the Leviathan State, to serve as a “civil theology” to restrain our anti-social self-interest … [Adam] Smith rejected Hobbes's malevolent view of man's nature as tied to debased anti-social passions. Men, for Smith, would adopt a rule of law because it in fact reflects humanity's commonly chosen morality.
Through social evolution, as Mandeville pointed out in The Fable of the Bees, men would recognize their frail but good human nature and freely choose those institutions that would confer social order and benefits.
So: human beings play games, and then human beings invent game theory (Von Neumann was probably too smart to be counted as human, but we’ll let that slide), then humans make computers to play games so that the humans can study game theory objectively.
Computers that play games can play a some games well: checkers, chess, backgammon. Others, not so well. Game theorists Koffer and Pfeffer explain (bolding is by me):
There have been far fewer successful programs that play games such as poker or bridge. We claim that this is not an accident. These games fall into two fundamentally different classes, and the techniques that apply to one do not usually apply to the other. The essential difference lies in the information that is available to the players. In games such as chess or even backgammon, the current state of the game is fully accessible to both players. The only uncertainty is about future moves. In games such as poker, the players have imperfect information: they have only partial knowledge about the current state of the game.
This can result in complex chains of reasoning such as: “Since I have two aces showing, but she raised, then she is either bluffing or she has a good hand; but then if I raise a lot, she may realize that I have at least a third ace, so she might fold; so maybe I should underbid, but . . . .” It should be fairly obvious that the standard techniques are inadequate for solving such games … In real life one rarely has perfect information. …
It is well-known in game theory that the notion of a strategy is necessarily different for games with imperfect information. In perfect information games, the optimal move for each player is clearly defined: at every stage there is a “right” move that is at least as good as any other move. But in imperfect information games, the situation is not as straightforward. In the simple game of “scissors-paper-stone,” any deterministic strategy is a losing one as soon as it is revealed to the other players.
This term of “perfect” vs. “imperfect” information is an important one. Now on to “singalling,” which for some reason is spelled in game theory literature with two Ls. To sum up, when you hear “perfect info,” think of checkers. When you hear “imperfect information,” think of “poker" or “life.”
The last important game theory term I’ll bother you with is signalling.
What is “signalling”? I’m not talking about turn signals or colored lights at intersections. I’m talking about singalling as it is used in game theory, economics, and biology.
The best short, simple intro is from Carl Bergstrom, writing about gazelles (bolding and underlining mine):
Grazing on the savannah, a gazelle spots a feline form moving through the tall grass fifty meters away. It lifts its head, listening and sniffing the breeze.
Released like a jack-in-the-box, it springs suddenly straight up into the air.
It lands, only to repeatedly leap in place, six feet high, again and again. Other members of the herd notice, and quickly begin to imitate its display.
A magpie alights at the edge of her nest, a juicy caterpiller dangling from her beak. Even before her feet touch the haphazard assembly of twigs, her four nestlings launch into a cacophany of squawks, warbles, clucks, and clackings.
As you are waiting for friend in the hotel lobby, a well-dressed man walks up and asks you for the time. You notice his thousand-dollar suit and, without thinking, address him as "Sir."
What, if anything, do these behaviors have in common?
The gazelle's leaping behavior, the nestlings' begging, the expensive suit - all of these things are signals. All are intended to convey information about a signaller, to a signal receiver. For humans, the fancy suit - like a fast car, an expensive bottle of wine, or a precious gemstone - indicates some property or quality of the signaller. In this case, that property might be the relative wealth of an individual.
Gazelles may be doing something similar with their jumping or "stotting" displays. Biologists have argued that the stotting display serves as a signal of quality to potential predators. "I'm a strong and healthy gazelle," the display demonstrates. "See how high I can jump? It would be a waste of your time and energy to chase after me!"
Baby birds, through their begging behavior, may be informing their parents about how badly they need to be fed. Additional examples are easy to find. Bull elk signal their quality to rivals and to potential mates with a large rack of antlers and a loud bugling call.
A peacock's fine tail serves to advertise the high quality of its bearer to potential mates.
These signals share an additional feature: all are costly to produce and send.
Expensive suits, fast cars, wine, or jewelery are not cheap in terms of that all-important human currency, money. Similarly, the stotting display is expensive - albeit in a different sort of currency - to the gazelle.
By leaping up and down, a gazelle is expending the very energy that it will need desperately should a chase ensue. Squawking to one's parents takes energy and may also alert predators to the location of a nest; producing and bearing a huge flashy tail is also energetically expensive, not to mention risky when predators are around.
Why do so many different species of animals all use signals that are inherently expensive, in a wide range of different signalling contexts?
Why not simply "whisper" the message to the intended receiver, rather than producing an elaborate and costly display?
And why do these expensive signals seem to be so convincing to the intended signal receivers?
An area of game theory called signalling theory examines the nature of communication behavior, and attempts to answer these sorts of questions.
Signalling theory can be applied broadly to human and non-human alike, and as such will be of interest to researchers in a wide range of fields, including biology, economics, sociology, anthropology, political science, communication studies, linguistics, philosophy, and psychology.
Wherever there are organisms, there are signals.
Whether you are walking through a forest, sitting in a meadow, or swimming along a coral reef, your senses are bombarded with messages, most of the produced by non-human signallers and intended for non-human receivers.
Calls, patterns, colors, fragrances - these are just a few of the modalities by which signals are sent and received.
To a certain degree these signals must be honest, at least on average.
After all, if they were not honest, the intended signal receivers would evolve to ignore them. And if signal receivers ignored these messages, they would be useless - and signallers would eventually evolve not to send them. But why do these signals stay honest? In the short run, at least, there would sometimes seem to be advantages to deception.
Much of honest signalling theory can be thought of as an attempt to answer this question.
Though the problem is simple to express, the solution is by no means obvious:
Two individuals have access to different information.
They could both gain if they could honestly share this information.
However, their interests do not coincide entirely, and so each has an incentive to deceive the other.
How can honest communication be ensured?
Interesting, eh?
If stotting is too new for you … consider Batman, as I often do.
After all, this is the importance of dressing up like a bat. Otherwise, he would no better than some grad student explaining economic-mathematical theories in pop culture language.
I suggest the phenomenon of signalling explains why the Galileo Affair happened – and what we can learn from it.
Returning to L (remember, L is our letter-stand in for the document Galileo’s 1615 Letter to the Grand Duchess Christina…):
Letter (L) is seen (correctly) as a philosophical statement by G regarding the different, non-overlapping magisteria (to borrow Gould’s phrase) of science and religion in human society.
However, I argue that L serves another purpose in addition to its function as a treatise; properly considered, L is polysemic. G’s L is meant to be a signal in the game theory sense: “I entreat those wise and prudent Fathers to consider with great care the difference that exists between doctrines subject to proof and those subject to opinion.”
The G-CC Game (GCCG) is a text that may be read as a tragicomedy of errors, of misread signals; the formal authorization of Dialogue and Bellarmine’s letter being the two most obvious examples. A review of all GCCG’s signalings is of course beyond the scope of this essay, but L seems a crucial signal, a missed opportunity in GCCG.
I argue GCCG was a variant of the iterated prisoner's dilemma, which began as a non-zero-sum game, but with imperfect information.
The “imperfect information” part of the description is crucial. Both G and CC attempted to signal the other at various stages throughout the game, only to have their signals misinterpreted or ignored. Furthermore, GCCG eventually became a noncooperative zero-sum engagement.
GCCG is a possible answer to the question “What happens in a game if there is a terrible misunderstanding in which another player seems to have defected from an agreement, but hasn't?”
In this light, GCCG may be read as a game theory parable of how a “saving face” strategy, when combined with a repeated misreading of signals sent by both parties, escalated into the worst possible conclusion for both players.
Concerning the text: I argue G is writing what an open letter, nominally addressed to an individual but intended for the consumption of moderate parties within CC. G refers to the common person's limited understanding in his argument for why the Bible cannot be read as a scientific treatise: the truths contained in the Bible were written for the general public.
Scientific truth was put second to getting the reader (or listener's) soul to heaven. While the above summary is true in a general sense, L is deeply equivocal in its rhetoric, by G’s design.
Consider: "These propositions uttered by the Holy Ghost were set down in that manner by the sacred scribes in order to accommodate them to the capacities of the common people, who are rude and unlearned."
Yet also in L: “The reason produced for condemning the opinion that the earth moves and the sun stands still in many places in the Bible one may read that the sun moves and the earth stands still.
Since the Bible cannot err; it follows as a necessary consequence that anyone takes an erroneous and heretical position who maintains that the sun is inherently motionless and the earth movable.”
G refers to the tempests “stirred up against me no small number of professors-as if I had placed these things in the sky with my own hands in order to upset nature and overturn the sciences."
Regarding Augustine: “These men would perhaps not have fallen into such error had they but paid attention to a most useful doctrine of St. Augustine's, relative to our making positive statements about things which are obscure and hard to understand by means of reason alone.”
On the surface, G’s method in writing to Christina is (ironically) the same method used by the Holy Spirit in writing the Bible: talk down. Yet I doubt that “talking down” to a Grand Duchess is G’s purpose.
The astronomer is following a rhetoric of epistolary composition, ars dictaminis, as described "The Medieval Art of Letter Writing: Rhetoric as Institutional Expression" by Les Perelman, according to custom set down in Bologna during the twelfth century: “A modified 'Approved Format' version of Murphy's table comparing the format presented in The Principles of Letter Writing with the Ciceronian six-part oration provides a vivid of the movement of the ars dictaminis away from a rhetoric illustration of persuasion toward a rhetoric of personal relationship.”
G, to my reading, follows the Bolognese form in writing to his social superior. It is unlike his tone in Dialogue. But why would a “Bolognese letter” read like a treatise, a rhetorical set-piece, and employ such strange loops of contradiction?
Given that the letter was created in response to a letter by Benedetto Castelli detailing a dinner argument – given that these words are written to a member of G’s patron family – given all mentioned above, we must read L as a signal in GCCG. In this reading, the apparent contradictions of GCCG are not errors, but G offering, in effect, terms: “I will leave the Bible alone if I am free to posit my physical, scientific speculations. However, I can defend myself, if need be. But I am not unreasonable; see, I am quoting Augustine. Furthermore, I understand your position, and am a good Catholic.”
But what happened to Galileo needn’t have occurred. This is not to excuse the church – even thought it had a cadre of reasonable, educated men who helped and were willing to protect Galileo, it was also a conservative institution trying to hold onto its power in the face of what it saw as a terrifying upheaval of tradition and God’s order. I am not offering any moral or ethical judgment.
What I do wonder about is why in situations of delicacy such as the Galileo Affair, both parties often end up with the worst of all possible worlds.
Short of Galileo being thrown into a dungeon or tortured by the Inquisition, it’s hard to see how the Church and the Astronomer could have handed each other a worse outcome.
On one side, a blind old man all but excommunicated, locked in his villa until death.
On the other side: a religious institution that for all its sins had been the source of intellectual life in Europe for a millennium getting with the (sadly deserved) mark of religious Cain to scientific Abel.
I think it was Burke that said the triumph of evil is that the good are often in conflict. Good men and women of God on one side. Good people of reason on the other. It needn’t be so. But it has been. It will be.
We are in a prisoner’s dilemma, a reiterated one, which started with Galileo and has not stopped until this day.
In the West, much as the Death of Socrates defined the relationship of Philosophy to Power, and the Death of Jesus of Nazareth defined the relationship of State to Church, the Trial of Galileo defined the relationship between Reason and Faith: War.
Maybe it would have happened anyway. Perhaps it was inevitable. Maybe the conflict gave both a kick in the pants: teaching Reason it couldn’t tie itself to authority to be safe, and telling Faith it needed to adapt and change to a new world. Maybe millennia from now, some far-seeing historian will read the history of GCCG and decide that, yes, that was the moment that Religion turned its gaze from physical explanation and temporal dominion to a higher, more elevated sphere; that when it gave up on enforcing physics, it began to fathom souls all the better. That Christianity yielded suzerainty over the outer world, and turned its gaze to the inner, leaving Reason the outer.
Perhaps the Galileo Game, the GCCG, was win-win after all.
Perhaps so.
But I wonder. The Galileo trial was the first meeting of Science and Faith.
And you know what they say about first impressions.
Galileo was the first modern scientist. His experience was novel, and formative. And it is remembered.
By me, for one.
Don’t you think this story is part of the reason that I’m on the side that I’m on? I say this not to argue my point, but to show how far this particular game, the GCCG Prisoner’s Dilemma has reached.
And even though I know better, Enlightenment secular humanists like myself will always see the shadow of the Church Militant in our nightmares, a harbinger of what will happen if society should lapse into the Sleep of Reason. If I may use an American example, we are like General Motors and the Union: rationally, we ought to be able to get along. But we have an acid history.
I think we all know how each group sees the other:
Maybe I’m exaggerating the conflict. Maybe the War’s over.
Even so. The lessons of the past remain, and we are as much held hostage by them as we are our current beliefs.
G. seems to have read the game theoretician Aesop’s story The Scorpion and the Frog:
A scorpion and a frog meet on the bank of a stream and the
scorpion asks the frog to carry him across on its back. The
frog asks, "How do I know you won't sting me?" The scorpion
says, "Because if I do, I will die too."The frog is satisfied, and they set out, but in midstream,
the scorpion stings the frog. The frog feels the onset of
paralysis and starts to sink, knowing they both will drown,
but has just enough time to gasp "Why?"Replies the scorpion: "It’s my nature..."
The man knew. And so in the letter, he writes: “Considering the force exerted by logical deductions, they may ascertain that it is not in the power of the professors of demonstrative sciences to change their opinions at will and apply themselves first to one side and then to the other.” L seems logically consistent if we expand its semantic space: we moderns need to see L not just as philosophy but also as a signal gambit in GCCG – one that, unfortunately, was missed.
By then it was too late.
