Sunday, May 24, 2009

The Hailstorm and a Difficult Line in Aristotle's Poetics

Lars Gustafsson

On the Hail storm of 88 and on a difficult line in Aristotle’s Poetics

On July 13th 1788 a series of extreme hailstorms killed people and livestock and devastated the entire crops over the entire Ile de France.

There is hardly any any work in poetics or in literary criticism which has had such a wide and profound influence as Aristotle’s Poetics.Make no mistake>it still exerts an influence on contemporary film and drama.
The Poetics contains a number of concepts and inventions of great importance to later work,specially in the French Classic drama,but also to dramaturgy in general.There is the doctrine of the unity of time,space and action.There is the difficult concept of catharsis or purification,obtained through the performance of tragic events,where it remains an open question whether Aristotle meant a mental purification of the onlooker,or something much more radical;tragic drama as a purification of the community as a whole.
Of special philosophical interest is another influential concept, the peripety or change of events.If you have access to a school edition of Racines “Phedre” where the lines are conveniently numbered and look up the very middle line of the drma,you will realize the extent to which the great French Dramatists of the Gold Age took Aristotle seriously.You will find that the central line is the one where it becomes clear to Phedra that her Housband ,supposed to be dead,has returned and her forbidden love to Hippolytos will be revealed:
“Madam,le roi qu’on a cru mort,va paraitre a vous yeux”

The concept of the peripety,or surprising change of events – if you prefer the word might be threshold – is of much wider interest than the purely dramaturgic one.Threshold events play an important role in political history,in ecology and in physics as well.
In a core passage of his book , found in Chapter XXV,(1461) Aristotle is approaching the question,still actual in modern criticism,to what extent the writer – an imitator of reality – is constrained by possibility and probability of the facts and the caracters he is dealing with:
respect to the requirements of art, a probable impossibility is to be preferred to a thing improbable and yet possible. Again, it may
be impossible that there should be men such as Zeuxis painted. 'Yes,'we say, 'but the impossible is the higher thing; for the ideal type
must surpass the realty.' To justify the irrational, we appeal towhat is commonly said to be. In addition to which, we urge that the irrational sometimes does not violate reason; just as 'it is probable
that a thing may happen contrary to probability.' “

It might seem that he is either stating a contradictory claim – the improbable is probable—or a triviality—that low probability events are possible. The line is a quotation from the minor tragedian Agathon ,well known from Platos dialogues and known for his elaborately entangled plots.There is no reason to assume that Aristotle is not supporting his claim .

Aristotle in general has a tendency to see the accidental,that which happens by mere chance, as beyond rational explanation.
”…the explanatory factors in events that occur by chance are indeterminate;and therefore chance is obscure to human calculation and is an accidental factor – but this
is,in the strict sense,an explanation of nothing. ”

(Metaphysics Kappa 1065b)

This is one of the central places where Aristotle differs from the modern.Probability theory is very much a product of the 17th and 18th centuries. Historically,Aristotles attempt to handle such concepts as possible,impossible,probable and improbable are in many respects admirable What is obviously lacking in the passage of the Metaphysics that I quoted is the view that probability, rationally treated, is about distributions of numbers of events,not a property of individual events.

From Pascal and onwards the unexpected has been a subject of controverse. There is the frequency view ,shared by Carnap and other philosophers, that probability expresses a relation between a least two variables,say the number of eyes on the dice and the number of throwings,and Ramseys view that probability of an individual ecent should be possible – given the apporopriate axiomatics – to be given a sense.
This is not the place to go deeper into that philosophical question,which in a way,constitutes sort of an ontological crack in the tradition of probability.( But let us keep in mind that if Carnap and his school is right – probability is exclusively about frequenciy we all,seen as individuals, lack probability.)
One great turning point is the invention of Gauss normal distribution, the curve resulting from Gauss density function. I remember the awe I felt when I first met this beautiful bellshaped curve. How could Nature know how to organise phenomena in such an elegant shape ? How come that the middle value between two extremes is the most frequent one ? From body weight in Stockholm to precipitation in Chicago ?
The beginner, like me in my early teens,looks with admiration at the big bell. Which is however not applicable to all of nature.The mathematically interested might be as interested in the fact that we are dealing with a partially convergent function. Which means that the flattening outskirts ,the areas beyond 99.73 % ,are infinitely convergent,or in other words,never reach zero.

”it is probable that a thing may happen contrary to probability”

Is it perhaps,something like this that Aristotle is talking about ? Of course ,the rare events in the flattening outskirts of the normal distribution,even when they are very rare,still must have a possibility. Otherwise they could not be part of a distribution whatsoever.But what would it mean,to say,like Aristotle,that it is probable that they occur?
If he had written;”it is possible” – we would have had no difficulty whatsoever.In fact – interpreted that way,the claim is trivial.But he seems to insist on ”probable”. Can there be probable improbabilities ?
Is it in the infinitely extended wastelands of the convergent parts of the function where his probable improbabilities have to be looked for ? Is it the two-headed calf and the 107 years old man Aristotle is looking for which sooner or later will appear if you lift the long veil of the Gauss distribution ? In what sense are they supposed to be probable ?

Very improbable events can happen. The big meteor or the mountain of gold are improbable but possible over time. The circular triangle is not possible and therefore cannot enter the discussion of the probable.
It might seem that either Aristotle means “possible” when he says “probable” or he makes a claim which is utter nonsense. As lack of consequence is not anything that Aristotle is frequently accused of ,we prefer to try an alternative interpretation.

In Book XV, ‘of the Poetics, there is an interesting passage which might provide a clue:

“ As in the structure of the plot, so too in the portraiture of character, the poet should always aim either at the necessary or the probable.
Thus a person of a given character should speak or act in a given way, by the rule either of necessity or of probability; just as this
event should follow that by necessary or probable sequence. It is therefore evident that the unraveling of the plot, no less than the
complication, must arise out of the plot itself, it must not be brought about by the Deus ex Machina- as in the Medea, or in the return of
the Greeks in the Iliad. The Deus ex Machina should be employed only for events external to the drama- for antecedent or subsequent events,
which lie beyond the range of human knowledge, and which require to be reported or foretold; for to the gods we ascribe the power of seeing
all things. Within the action there must be nothing irrational. If the irrational cannot be excluded, it should be outside the scope of the tragedy. Such is the irrational element in the Oedipus of Sophocles.”

In this passage two new concepts are entering the discourse;the necessary and the rational with their respective counterparts the irrational and that which cannot be unravelled by necessary or probable sequence.The fundamental idea – it seems – is that the plot of the tragedy should be derived from its own elements and not from divine interference.
Sofokles Oidipus Rex is brought forward as an example of nothing irrational being essential to the developement of the tragedy.
The example is very well chosen. It has often been observed by different readers that the sequence of events which leads the unhappy king to commit the two most serious crimes known to classic Greek conscience,to murder his father and to marry his mother,is by no means a mechanic trajectory,the end of which can be effectively calculated from the initial conditions.
King Oidipus is not a missile.He is an agent.He makes choices.And for each choice he makes,he takes another step closer to catastrophy.His tragedy is self-made.

Operating inside the repertory of possibilities which the scope of the drama contains,Oidipus seals his own destiny.The Gods knew it .Because the Gods ,who observe ,as it where the frozen space time of physics,knew all the choices he would make.
But it is Oidipus who made the choices.This is not the type of determinism which is incompatible with free choice.It is a theory which includes the choices as a part of – as Aristotle puts it – “its scope”.

The surprise is that a situation the make-up of which seemingly contains only probable elements is able to produce out of them the improbable,the surprising,the catastrophic.
So where is the element of surprise ? Where is the heart of our discussion ?

“Planning for uncertainty” is a sort of password often heard in the confronting the contingencies of the modern world.
The “futurology” discussions of the 1960’ s often seemed to get stuck in the intricacies of trend extrapolation. If my excentric uncle seems to have doubled his wisky intake every week the last winter it seems inevitable that there will come a week when he is consuming a bathtube of wisky.Or is it not ? Does the trend contain its own disproof – “das Andere von sich selbst” Hegel perhaps would have put it.
It is quite surprising to see to what a large extent the primitivities of trend extrapolation are still dominating the discussions of global warming and climate change.
To plan for uncertainty,or to predict the improbable ,we obviously need something more refined,something like the board of chess and the chessmen. Which contains all the possible surprises of the game.What are we doing when we play chess ?

The hailstorms ofJuly 1788 was a major economic catastrophee which,at a time when a third of an artisan income was needed to obtin bread,led to a surge in bread p[rices imposible to hande.The storms deprived the Minister of Finance M.Neckar of any hope to be able to handle an already precaiou econom situation.
Did a set of hailstorms trigger the French Revolution ? I do not know.Nobody knows.
The elements of surprise – like in the Aristotelian tragedy -
are all derivable from inside the rules and the operations of the game. There is the syntactically impossible, which the beginner soon learns to master and there is the strategically impossible.
The similarity to language – vocabulary,grammar,syntax – is obvious. And there is a similarity to games, e.g. chess,where the activity consists in looking for the possible and the threat is in the impossible.
There are other possible analogies.E.g. - are we able to surprise ourselves ? This is the point of assuming ,like Leibniz or Sigmund Freud that there are constituents of mental life of which we are not immediately aware.
So a reasonable interpretation of Aristotles
'it is probable
that a thing may happen contrary to probability.'
might be that any situation which has the sufficient amount of complexity might produce the completely unexpected.
An event or a developement can hardly be described as “unexpected” if there is not an expectation of a different outcome.

A certain historical bias has brought us to believe that events like The French Revolution where necessary parts of an historical scenario.This might to some extent be due to a misunderstood evolutionary scheme,such as we find it in Hegels philosophy,as developed in in “Phenomenologie des Geistes”. And certainly,the intensionalism of an older religiously inspired historicism lures in the background.
In the retrospective,the French Revolution took place because it had to be. But does that have to be the case ? Are we under the influence of the narrative,which makes us neglect all the other possibilities of a situation ? It seems fairly clear that to contemprary witnesses most of it came as a surprise or a series of surprises. The view of the French Revolution as a necessary step towards some future historical state is of course a metaphysical idea.
A stochastic view of historical phenomena ,like for that part biological phenomena, may be even the physical facts about the universe as whole,seems in a profound way to break with our metaphysical preconceptions.As Ulf Danielsson has observed in a recent Swedish publication ,it might seem that the comparatively greater progress in modern biological disciplines, compared to the situation in physics ,might have to do with a greater liberation from the idea of a preconceived scenario.
What would it mean to say :“It could have taken another direction” ?

The philosophical analysis needs some care.There is a logical trap here which should be avoided:
There is the well-known puzzle with counterfactuals:If Cleopatras nose had been an inch longer or if Louis XVI had been an intelligent monarch surrounded by intelligent advisers , world history would have taken another course so and so.The First World War might have been avoided if the Ems Telegram had never been sent,and by consequence the Second World War had not taken place either.The genre is well-known.And has of course led to philosophical controverse.
A view to which I tend to lean is that counterfactuals are nonsense.And the reason is that the antecedent in a proposition of the form
If P had not been the case,so non-Q
where the negation,non-P,as an historical fact is false.And from a false proposition any proposition follows.So the counterfactual can prove any proposition which means that it can prove no proposition at all.
Counterfactual conclusions are no conclusions at all.Logically,they are nonsense.
However,there is more to it.
Propositions like “It could have taken another direction” or “it could have been otherwise” ,”are nonsense. They are not counterfactual;they simply say something about the facts and its inherent possibilities.It is the expression of a stochastic or probability-oriented approach to an event.The situation in France in the summer of 1789 contained elements which made the French revolution possible.And it took place. But only the hegelian has to claim this as a historical necessity. A different outcome was statistically possible.
At the heart of Leibniz’ philosophy is a concept of mutually compatible facts,or in his own language;compatibilia.
The fact that the cat is on the carpet is compatible with the dog being in the kitchen – at least it might seem so. But the cat being on the carpet is not compatible with the cat being in the garden.
It is not quite clear whether Leibniz meant that facts could contradict each other in their own right,or that descriptions of possible facts can be contradictory.It is of less importance in this context – so I shall set that question aside, and by compatibles simply mean states of affairs,the descriptions of which are not contradictory.
Leibniz world – the existing world - is the juxtaposition of the greatest possible number of compatibilia. Why he believes that the universe needs the highest possible amount of factual density has never become quite obvious to me.
But the concept of compatibilia is obviously useful in probability .A particular outcome of two dices,does not logically exclude another outcome as long as it belongs to the fundamental repertory of the game.
Or in other words, the existence of a post-facto narration, exerts a profoundly misleading influenceit lures us into the illusory beleif that there was an ante-factum narratives.There were many ,and they were logically interchangable.
The situation inJuly 1789 contained a probably very big number of elements which ,where compatible – of course with what actually happened – the fast development from monarchy to republic from republic to the Jacobine horror and from Jacobine horor rule to military dictatorship - but also with another outcome; say ,constitutional monarchy.
Assume that this really had taken place instead of the succession of dramatic events which is called the French Revolution –would we be able to see that the situation also contained that possibility ? I am not certain at all.Would we have observed the inherent possibilities of a Great and devastating war in August 1914 if the war had never taken place.I am not certain at all.

Seminar on Surprises arrangedby The Royal Swedish Academy of Science Abisko Institute of Polar Research May 2009

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