Fallet Guillou
Jan Guillou är ett tragiskt fall.Vad jag bevittnar gör mig egentligen bara ledsen.Den unge man som en gång väckte vår odelade beundran genom att vägra söka nåd hos IB-affärens cyniska regering, och som utstod ett år i fängelse hellre än att söka nåd och därmed moraliskt sanktionera statsmakternas rätt att avlyssna och registrera medborgarnas åsikter, har nu förvandlats till en högröstad och vulgär åsiktspolis med den nya medborgarrättsrörelsen högst upp på en brokig lista av fiender.
Hans utveckling har inte varit bra. Publika framgångar med litterär våldsunderhållning har gjort honom stöddig .Helst borde man kanske förbigå honom med hänsynsfull tystnad.
Men i sin dumma och onödigt högmodiga artikel i Aftonbladet i söndags ( 7.6.09)bidrar han aktivt till ett intellektuellt missförstånd som dock i allmänt intresse måste förebyggas.Den nya medborgarrättsrörelse som nu bryter fram på många olika håll i det publika rummet och senast tog sig uttryck i Piratpartiets spektakulära framgång i Europavalet, är en integritetsrörelse.( Herr Reinfeldt har ännu inte fattat vad som berövade honom all framgång i EU-valet;det var hans återstående liberaler som omedelbart reagerade på FRA-lagen)
Den går inte,som Herr Guillou egendomligt nog tycks tro, ut på att legitimera stöld av upphovsrätter.Den är en försvarsrörelse för hotade medborgarrätter ,i princip samma slags rätter som Jan Guillou en gång i tiden så modigt försvarade.
Med upphovsrätterna är det så, att när en revolutionerande teknologi förändrar deras förutsättningar måste de anpassas till den på ett sådant sätt att fönstret inte öppnas för en polisstat. Det finns naturligtvis i det längre perspektivet lösningar som inte leder till en ny IB-affär.
Det var alltså det Piratpartiet handlade om, Stupid !
Att Guillou inte inser detta vittnar, antingen om att hans intellektuella gåvor inte riktigt är vad de har varit, eller att han har förvandlats till en grovhudad självupptagen cyniker.
Kanske är det nu dags att han tar med sig sin Plåt- Nicklas,Riddare Arnt, och rider bort i den solnedgång som är kiosklitteraturens sorgliga öde.
Tuesday, June 9, 2009
Monday, June 1, 2009
LIBERT,INTEGRITY,DEFENSE OF THE NET
According to an ancient source, the Emperor of Persia gave orders that the waves of the sea must be punished by beating, as the storm hindered him from transporting his troups by ship.
That was quite stupid of him. Today, would he maybe have tried with Stockholm district court? Or a consultative conversation with the judge?
It is odd, how strongly the situation spring 2009 – on the area of civil rights – reminds about the struggles over freedom of press in France, during the decades preceding the French revolution.
A new world of ideas is emerging and would not have been able to, were it not for an accelerating technology.
Raids against secret printing houses, confiscated pamphlets and – even more – confiscated printing equipment. Orders of arrest and adventurous nightly transports between Prussian enclave Neuchâtel – where not only large parts of the Encyclopedia was produced, but also lots of daring pornography, between the atheist pamphlets – and Paris.
Between the 1730’s and 1780’s, the number of state censors in France was doubled by four. The raids against illegal printing houses was rising at about the same pace. In retrospect, we know it did not help. Rather, the increase of censorship and printing house raids had a stimulating effect on the new ideas and made them spread even faster.
Now the conflict rage over the net’s continued existence as a forum of ideas and as an institution of civil rights, protected from privacy-threatening interventions and against powerful private interests.
That a mad French-German proposal just fell in the European parliament does certainly not mean that the freeedom of the net and the privacy is now safeguarded.
Hur real are then these threats? Let us think about the Dalälven river in spring flood times. A really critical year, the water may trespass 100 meters, maybe 200 meters, into house lots and meadows. Does it help to call the Ludvika police?
So for – this is shown by most historical experience – legislation has never been able to stop technological development.
Walter Benjamin wrote an influential essay, whose title usually is translated as “The Work of Art in the Age of Mechanical Reproduction“, where he draws a series of interesting conclusions about what the radical changes that must follow on his time’s relatively modest degree of reproducibility. The digital revolution has brought about a reproducibility which Walter Benjamin could hardly ever have dreamt about. One could talk about maximal reproducibility. Google is about to build a library that, if is is allowed to grow, will make most material libraries obsolete or at least outmoded.
Cinema and paper newspapers are since long drawn into this new immateriality. Films, novels, magazines let themselves be reproduced. Further on; also three-dimensional objects, like products of programmable lathes let themselves be reproduced. Wirelessy and rapidly.
This immaterialisation naturally threatens the material copyright. And then were are not only talking about run-of-the-mill writers like Mr. Jan Guillou, whose social problems of acquiring new country estates I am honestly ignoring.
Material copyright has much more serious aspects: What has the large pharmaceutical firms patents on aids medicin meant for the third world? Or what about Monsanto’s claim of holding rights on crops and pigs?
Every society must make its balance between differing interests and every hypocritic attempt to ignore that is nonsense. A functioning military defence is more important than ice hockey rinks and bicycle lanes. Probably the net implies a threat against the copyright of the material. And so what?
Intellectual and personal integrity for the citizens, briefly speaking an internet that has not been transformed into a government channel by lobby-marinated courts and EU politicians in leashes, is arguably more important than the needs of a primarily industrial scene of literarature and music, which is rapidly crumbling away already within the lifetime of the authors. The need of being read, of influenceing, to formulate one’s times, may but does not need to get in conflict with the wish to sell many copies. When the both needs are getting in conflict, the industrial interest must be put aside and the great intellectual sphere of the arts must be defended against threats.
The essential interest of artists and authors, given that they are intellectually and morally serious in hat they are doing, must certainly be to get read, to let their voice become heard in their generation. How that goal is attained, that is, how to reach the readers, is in this perspective of secondary importance.
The growing defence of the internet’s expanded freedom of speech, of the immaterial civil rights, that we are now witnessing in country after country, is the start of an – just as the last time in the early 18th century – liberalism that is carried by technology and therefore emancipated.
Therefore, my vote in the elections to the European Parliament goes to the Pirate Party.
Trnslation by Rasmus Fleischer
That was quite stupid of him. Today, would he maybe have tried with Stockholm district court? Or a consultative conversation with the judge?
It is odd, how strongly the situation spring 2009 – on the area of civil rights – reminds about the struggles over freedom of press in France, during the decades preceding the French revolution.
A new world of ideas is emerging and would not have been able to, were it not for an accelerating technology.
Raids against secret printing houses, confiscated pamphlets and – even more – confiscated printing equipment. Orders of arrest and adventurous nightly transports between Prussian enclave Neuchâtel – where not only large parts of the Encyclopedia was produced, but also lots of daring pornography, between the atheist pamphlets – and Paris.
Between the 1730’s and 1780’s, the number of state censors in France was doubled by four. The raids against illegal printing houses was rising at about the same pace. In retrospect, we know it did not help. Rather, the increase of censorship and printing house raids had a stimulating effect on the new ideas and made them spread even faster.
Now the conflict rage over the net’s continued existence as a forum of ideas and as an institution of civil rights, protected from privacy-threatening interventions and against powerful private interests.
That a mad French-German proposal just fell in the European parliament does certainly not mean that the freeedom of the net and the privacy is now safeguarded.
Hur real are then these threats? Let us think about the Dalälven river in spring flood times. A really critical year, the water may trespass 100 meters, maybe 200 meters, into house lots and meadows. Does it help to call the Ludvika police?
So for – this is shown by most historical experience – legislation has never been able to stop technological development.
Walter Benjamin wrote an influential essay, whose title usually is translated as “The Work of Art in the Age of Mechanical Reproduction“, where he draws a series of interesting conclusions about what the radical changes that must follow on his time’s relatively modest degree of reproducibility. The digital revolution has brought about a reproducibility which Walter Benjamin could hardly ever have dreamt about. One could talk about maximal reproducibility. Google is about to build a library that, if is is allowed to grow, will make most material libraries obsolete or at least outmoded.
Cinema and paper newspapers are since long drawn into this new immateriality. Films, novels, magazines let themselves be reproduced. Further on; also three-dimensional objects, like products of programmable lathes let themselves be reproduced. Wirelessy and rapidly.
This immaterialisation naturally threatens the material copyright. And then were are not only talking about run-of-the-mill writers like Mr. Jan Guillou, whose social problems of acquiring new country estates I am honestly ignoring.
Material copyright has much more serious aspects: What has the large pharmaceutical firms patents on aids medicin meant for the third world? Or what about Monsanto’s claim of holding rights on crops and pigs?
Every society must make its balance between differing interests and every hypocritic attempt to ignore that is nonsense. A functioning military defence is more important than ice hockey rinks and bicycle lanes. Probably the net implies a threat against the copyright of the material. And so what?
Intellectual and personal integrity for the citizens, briefly speaking an internet that has not been transformed into a government channel by lobby-marinated courts and EU politicians in leashes, is arguably more important than the needs of a primarily industrial scene of literarature and music, which is rapidly crumbling away already within the lifetime of the authors. The need of being read, of influenceing, to formulate one’s times, may but does not need to get in conflict with the wish to sell many copies. When the both needs are getting in conflict, the industrial interest must be put aside and the great intellectual sphere of the arts must be defended against threats.
The essential interest of artists and authors, given that they are intellectually and morally serious in hat they are doing, must certainly be to get read, to let their voice become heard in their generation. How that goal is attained, that is, how to reach the readers, is in this perspective of secondary importance.
The growing defence of the internet’s expanded freedom of speech, of the immaterial civil rights, that we are now witnessing in country after country, is the start of an – just as the last time in the early 18th century – liberalism that is carried by technology and therefore emancipated.
Therefore, my vote in the elections to the European Parliament goes to the Pirate Party.
Trnslation by Rasmus Fleischer
Tuesday, May 26, 2009
Att Prygla Älvens Stigande Vatten: Om Nätets Frihet och Integritet.
Storkonungen av Persien skall,enligt en antik källa,ha låtit prygla havets vågor för att stormen hindrade honom att föra trupper över havet.
Det var dumt av honom.Idag hade han kanske försökt med Stockholms Rådhusrätt ? Efter ett rådgivande samtal med domaren ?
Det är egendomligt,hur starkt situationen våren 2009 - på medborgarrättens område – påminner om den franska tryckfrihetens öden under de decennier som föregick franska revolutionen.
En ny idévärld växer fram och den skulle inte ha kunnat göra det utan att bäras av en allt snabbare utvecklad teknologi.
Razzior i hemliga tryckerier, beslagtagna tryckalster och - än mer - beslagtagen tryckeriutrusting.Arresteringsbrev och äventyrliga nattliga transporter mellan preussiska enklaven Neuchâtel - där inte bara en stor del av delarna i Encyklopedin kom till,utan också åtskillig djärv pornografi mellan de ateistiska pamfletterna – och Paris.
Mellan cirka 1730 och 1780-talet fyrdubblades antalet statliga censorer i Frankrike och beslagen mot illegala tryckerier växte i ungefär samma tempo.Som vi vet nu ,hjälpte det inte.Snarare verkade censurens och tryckerirazzians tillväxt stimulerande på de nya idéerna och satte ordentlig fart på deras utbredning.
Nu gäller det Nätets fortsatta existens som idéforum och som medborgarrättslig institution,skyddad mot identitetskränkande ingrepp och skyddad mot mäktiga enskilda intressen.
Att ett fransk-tyskt dårförslag just har fallit i Europaparlamentet innebär inte att nätfrihet och integritet på något sätt är tryggade.
Hur reella är egentligen dessa hot ? Låt oss tänka oss Dalälven i vårflodstider.Ett verkligt kritiskt år ,där vattnet tar sig in 100 meter,200 meter in på villatomter och strandängar.Hjälper det att ringa efter ludvikapolisen ?
Hittills – det visar det mesta av den historiska erfarenheten – har lagstiftning aldrig kunnat stoppa teknologisk utveckling.
Walter Benjamin skrev en inflytelserik essä vars titel brukar översättas som ”Konstverket i reproduktionsåldern” där han drar en rad intressanta slutsatser om den radikala förändring som hans tids relativt anspråkslösa reproducerbarhet innebar. Den digitala revolutionen har medfört en reproducerbarhet som Walter Benjamin knappast kan ha drömt om.Man skulle kunna tala om den maximala reproducerbarheten.Google håller på att bygga ett bibliotek,som,om det får växa,kommer att göra det mesta av de materiella biblioteken obsoleta eller i varje fall antikverade.Biografen och papperstidningen är sedan rätt länge indragna i denna nya immaterialitet.
Filmer,romaner,tidskrifter låter sig reproduceras.Inte nog med det; även tredimensionella föremål, till exempel produkter från programstyrda svarvar låter sig reproduceras .Trådlöst och snabbt.Denna immaterialisering innebär naturligtvis ett hot mot den materiella upphovsrätten. Och vi talar då inte bara om det uppenbara hotet mot herrar Guillous och de andra dussinförfattarnas möjligheter att att lägga sig till med nya herrgårdar,ett socialt problem som jag uppriktigt sagt ger en god dag.
Materiell upphovsrätt har mycket allvarligare sidor än så:vad har de stora läkemedelsfirmornas upphovsrätt till AIDS—formler betytt för Tredje Världen ? Eller vad sägs om Santos anspråk på den materiella upphovsrätten till grödor och grisar ?
Allt samhällsliv kräver en avvägning mellan olika intressen och alla hycklande försök att dribbla bort detta är nonsens.En fungerande försvarsmakt är faktiskt viktigare än ishockeyplaner och cykelbanor.Förmodligen innebär nätet ett hot mot den materiella upphovsrätten.
And so what ?
Intellektuell och personlig integritet för medborgarna ,kort sagt ett internet som inte har förvandlats till en myndighetskanal av lobbypreparerade domstolar och EU-politiker i halskoppel,är rimligtvis viktigare än behoven hos en i huvudsak industriell litteratur- eller musikscen som snabbt förvittrar till makulatur redan i upphovsmännens egen livstid. Behovet av att bli läst,att påverka,att formulera sin samtid behöver inte men kan råka i konflikt med önskan att sälja många exemplar.När det blir konflikt mellan båda måste det industriella intresset vika och konstens stora intellektuella sfär försvaras emot allt som hotar den.
Det väsentliga intresset för konstnärer och författare som tar sin verksamhet på intellektuellt och moraliskt allvar måste naturligtvis vara att bli lästa,att göra sig hörda i sin generation.Hur man blir läst,d.v.s. hur man når läsarna,är i detta perspektiv sekundärt.
Det växande försvar av nätets utvidgade yttrandefrihet ,alltså av de immateriella medborgarrätterna som vi nu ser
i land efter land,är början till ,en precis som förra gången på sjuttonhundratalet,teknikburen, och därför befriad ,liberalism.
Jag kommer att rösta på Piratpartiet i 2009 års europaval.
Det var dumt av honom.Idag hade han kanske försökt med Stockholms Rådhusrätt ? Efter ett rådgivande samtal med domaren ?
Det är egendomligt,hur starkt situationen våren 2009 - på medborgarrättens område – påminner om den franska tryckfrihetens öden under de decennier som föregick franska revolutionen.
En ny idévärld växer fram och den skulle inte ha kunnat göra det utan att bäras av en allt snabbare utvecklad teknologi.
Razzior i hemliga tryckerier, beslagtagna tryckalster och - än mer - beslagtagen tryckeriutrusting.Arresteringsbrev och äventyrliga nattliga transporter mellan preussiska enklaven Neuchâtel - där inte bara en stor del av delarna i Encyklopedin kom till,utan också åtskillig djärv pornografi mellan de ateistiska pamfletterna – och Paris.
Mellan cirka 1730 och 1780-talet fyrdubblades antalet statliga censorer i Frankrike och beslagen mot illegala tryckerier växte i ungefär samma tempo.Som vi vet nu ,hjälpte det inte.Snarare verkade censurens och tryckerirazzians tillväxt stimulerande på de nya idéerna och satte ordentlig fart på deras utbredning.
Nu gäller det Nätets fortsatta existens som idéforum och som medborgarrättslig institution,skyddad mot identitetskränkande ingrepp och skyddad mot mäktiga enskilda intressen.
Att ett fransk-tyskt dårförslag just har fallit i Europaparlamentet innebär inte att nätfrihet och integritet på något sätt är tryggade.
Hur reella är egentligen dessa hot ? Låt oss tänka oss Dalälven i vårflodstider.Ett verkligt kritiskt år ,där vattnet tar sig in 100 meter,200 meter in på villatomter och strandängar.Hjälper det att ringa efter ludvikapolisen ?
Hittills – det visar det mesta av den historiska erfarenheten – har lagstiftning aldrig kunnat stoppa teknologisk utveckling.
Walter Benjamin skrev en inflytelserik essä vars titel brukar översättas som ”Konstverket i reproduktionsåldern” där han drar en rad intressanta slutsatser om den radikala förändring som hans tids relativt anspråkslösa reproducerbarhet innebar. Den digitala revolutionen har medfört en reproducerbarhet som Walter Benjamin knappast kan ha drömt om.Man skulle kunna tala om den maximala reproducerbarheten.Google håller på att bygga ett bibliotek,som,om det får växa,kommer att göra det mesta av de materiella biblioteken obsoleta eller i varje fall antikverade.Biografen och papperstidningen är sedan rätt länge indragna i denna nya immaterialitet.
Filmer,romaner,tidskrifter låter sig reproduceras.Inte nog med det; även tredimensionella föremål, till exempel produkter från programstyrda svarvar låter sig reproduceras .Trådlöst och snabbt.Denna immaterialisering innebär naturligtvis ett hot mot den materiella upphovsrätten. Och vi talar då inte bara om det uppenbara hotet mot herrar Guillous och de andra dussinförfattarnas möjligheter att att lägga sig till med nya herrgårdar,ett socialt problem som jag uppriktigt sagt ger en god dag.
Materiell upphovsrätt har mycket allvarligare sidor än så:vad har de stora läkemedelsfirmornas upphovsrätt till AIDS—formler betytt för Tredje Världen ? Eller vad sägs om Santos anspråk på den materiella upphovsrätten till grödor och grisar ?
Allt samhällsliv kräver en avvägning mellan olika intressen och alla hycklande försök att dribbla bort detta är nonsens.En fungerande försvarsmakt är faktiskt viktigare än ishockeyplaner och cykelbanor.Förmodligen innebär nätet ett hot mot den materiella upphovsrätten.
And so what ?
Intellektuell och personlig integritet för medborgarna ,kort sagt ett internet som inte har förvandlats till en myndighetskanal av lobbypreparerade domstolar och EU-politiker i halskoppel,är rimligtvis viktigare än behoven hos en i huvudsak industriell litteratur- eller musikscen som snabbt förvittrar till makulatur redan i upphovsmännens egen livstid. Behovet av att bli läst,att påverka,att formulera sin samtid behöver inte men kan råka i konflikt med önskan att sälja många exemplar.När det blir konflikt mellan båda måste det industriella intresset vika och konstens stora intellektuella sfär försvaras emot allt som hotar den.
Det väsentliga intresset för konstnärer och författare som tar sin verksamhet på intellektuellt och moraliskt allvar måste naturligtvis vara att bli lästa,att göra sig hörda i sin generation.Hur man blir läst,d.v.s. hur man når läsarna,är i detta perspektiv sekundärt.
Det växande försvar av nätets utvidgade yttrandefrihet ,alltså av de immateriella medborgarrätterna som vi nu ser
i land efter land,är början till ,en precis som förra gången på sjuttonhundratalet,teknikburen, och därför befriad ,liberalism.
Jag kommer att rösta på Piratpartiet i 2009 års europaval.
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:
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
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:
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
Saturday, May 16, 2009
Portraits
My son Benjamin has been kind enough to shoot a series of portraits during my visit to Austin. I share them below.
For reproduction rights, please contact him at Bgustafsson86@hotmail.com
For reproduction rights, please contact him at Bgustafsson86@hotmail.com
Sällsamma kretslopp och radikala veck
Topologins ord för veckbilningar är involutioner; operationer där en avbildning eller mapping, mångfaldigt avbildas in i sig själv.Som den gamla ,högst fascinerande,reklametiketten på min barndoms burkar med skurmedlet Tomteskur.Etiketten föreställde en tomte som höll en exakt likadan burk Tomteskur i handen. O.s.v. in i en förminskning som ögat inte längre kunde uppfatta.
Talsystemet kan avbildas in i sig självt på många olika sätt.Till exempel så att varje heltal tillordnas det efterföljande. Detta kan upprepas oändligt många gånger om varje avbildning börjar ett steg (ett heltal) efter det där den föregående avbildningen började:
1 2 3 4 5 6….
1 2 3 4 5 6…
1 2 3 4 5 6….
Heltalsserien rymmer hur många avbildningar som helst av sig själv .Och detta är just Cantors definition av en transfinit mängd. Den är ekvivalent med alla sina äkta delmängder.
”He’s dreaming now,”said Tweedledee:and what do you think he’s dreaming about ?”
Alice said ”Nobody can guess that.”
”Why,about you !” Tweedledee exclaimed,clapping his hands triumphantly.
”And if he left off dreaming about you ,where do you suppose you’d be?”
”Where I am now,of course,”said Alice.
”Not you!” Tweedledee retorted contemptuosly.”You’d be nowhere.Why,you’re only a sort of things in his dream!”
”If that there King was to wake,added Tweedledum,”you’d go out –bang!-just like a candle!”
Det börjar redan hos Cervantes.I tredje kapitlet av andra delen av Don Quijote dyker det upp en pratsam och entusiastisk herre,ungkarlen Sanson Carrasco,som skattar sig lycklig att ha träffat hjältarna i en så berömd roman.
”Don Qijote bad honom åter resa sig ’ Är det verkligen sant,frågade han sedan ,’att det finns en bok om mig och att någon morisk lärd skrev den ?’
’För att visa dig hur sant det är,svarade Sanson ,kan jag säga dig att det är min uppfattning att det föreligger idag mer än tolv tusen exemplar av den berättelsen. ’
Och för en alltmer häpnande Don Quijote fortsätter ungkarlen att utlägga romanens förtjänster och framgångar.Vad som sker är med andra ord att en roman avbildas in i en roman. Hjältarna möter sig själva men denna gång som sina egna litterära avbildningar.Omedvetna om att de också själva är avbildningar.
Nästa station är hos Lewis Carroll,Alices möte med den sovande röde kungen i ”Through the Looking-Glass”.Bröderna Tweedledee och Tweedledum varnar henne mycket allvarligt för att väcka den snarkande kungen som ligger utsträckt i gräset.Som den ordentliga flicka hon är oroar hon sig nämligen för att kungen kanske kan förkyla sig.
’Han drömmer nu’sade Tweedledee:’och kan du tro vad han drömmer om ?’
Alice sade ’Det kan ingen gissa.’
’Jo just om dig’ ropade Tweddledee’ och slog ihop händerna i triumf.’Och ifall han skulle sluta drömma om dig,kan du tänka dig var du skulle hamna då ?”
’Där jag är nu,naturligtvis ’sade Alice.
’Inte du’ genmälde Tweedledee spydigt.’Du skulle inte vara någonstans.Du är bara något slags nånting i hans dröm’
Denna underbara nonsensdialog når en höjdpunkt när Alice påpekar att, om hon är en beståndsdel i den röde Kungens dröm,kan hon knappast heller väcka honom.
Om vi uppfattar de båda delarna av Don Quijote som en enda berättelse, har vi alltså att göra med en berättelse som viks in i sig själv.Vilket skapar osäkerhet om vad som är representationen och vad som är det representerade .I fallet med den sovande röde kungen är det,än mer raffinerat,en dröm som har vikts in i sig själv.
Den tredje klassiker som hängivet ägnar sig åt detta slags konst är Jorge Luis Borges.”Den cirkelformade ruinen” är bara en av de ”Ficciones” där han utforskar detta slags världar som mynnar ut i sig själva.
Vikningar och veckbildningar är i själva verket ytterst intressanta operationer.
Möbiusbandet med dess sällsamma slinga bildar bara en enda yta,Kleins flaska,inte fullt realiserbar i det tredimensionella rummet, har en insida som är dess utsida och vice versa;den påminner med andra ord om vår jordiska existens;vi är inneslutna i ett rum som vi inte kan lämna. Ett argument mot dödsskräck.
Kurt Gödel bevisar att Principia Mathematica och liknande system måste innehålla inom systemet formellt oavgörbara satser.Och sättet att visa detta är med så kallade Gödelnumren.Gödel avbildar matematiken i dess helhet på ett hörn av matematiken genom att ge varje tecken som kan förekomma i en välbildad formel dess unika signum i form av ett tal. Därmed kan hela beviset ges en matematisk behandling.
Denna geniala veckbildning för oss till Douglas Hofstaedters fascinerande böcker, ”Gödel,Escher, Bach” från 1979 och ”I am a strange loop” 2007.Hofstaedter tolkar ett klassiskt filosofiskt problem ,självmedvetandet,som resultatet av en vikning eller en ”strange loop”. Mitt medvetande är en mer eller mindre bristfällig avbildning av världen.Men i denna avbildning finns också avbildningen av mig själv. Eller som den amerikanska flickan säger i ”Den amerikanska flickans söndagar” :
Hur kan vi tala till oss själva
och lyssna som vore det en annan?
Är vi kanske,nogra räknat,mer än en ?
Hur många av oss bor i samma magra kropp ?
Och detta sällsamma som spegeln säger,
att allt det som är jag hör till
en yttre värld som frågar föga efter mig.
Och samtidigt är hela denna yttervärld
det enda som min innervärld består av .
Världen,sinnrikt vikt in i sig själv.
Det är vad spegeln säger.Men kan
då delen vara helheten som i sin tur
är delen ?Någonting är konstigt här.
Jag tror inte alls att vi har fattat världen.
Talsystemet kan avbildas in i sig självt på många olika sätt.Till exempel så att varje heltal tillordnas det efterföljande. Detta kan upprepas oändligt många gånger om varje avbildning börjar ett steg (ett heltal) efter det där den föregående avbildningen började:
1 2 3 4 5 6….
1 2 3 4 5 6…
1 2 3 4 5 6….
Heltalsserien rymmer hur många avbildningar som helst av sig själv .Och detta är just Cantors definition av en transfinit mängd. Den är ekvivalent med alla sina äkta delmängder.
”He’s dreaming now,”said Tweedledee:and what do you think he’s dreaming about ?”
Alice said ”Nobody can guess that.”
”Why,about you !” Tweedledee exclaimed,clapping his hands triumphantly.
”And if he left off dreaming about you ,where do you suppose you’d be?”
”Where I am now,of course,”said Alice.
”Not you!” Tweedledee retorted contemptuosly.”You’d be nowhere.Why,you’re only a sort of things in his dream!”
”If that there King was to wake,added Tweedledum,”you’d go out –bang!-just like a candle!”
Det börjar redan hos Cervantes.I tredje kapitlet av andra delen av Don Quijote dyker det upp en pratsam och entusiastisk herre,ungkarlen Sanson Carrasco,som skattar sig lycklig att ha träffat hjältarna i en så berömd roman.
”Don Qijote bad honom åter resa sig ’ Är det verkligen sant,frågade han sedan ,’att det finns en bok om mig och att någon morisk lärd skrev den ?’
’För att visa dig hur sant det är,svarade Sanson ,kan jag säga dig att det är min uppfattning att det föreligger idag mer än tolv tusen exemplar av den berättelsen. ’
Och för en alltmer häpnande Don Quijote fortsätter ungkarlen att utlägga romanens förtjänster och framgångar.Vad som sker är med andra ord att en roman avbildas in i en roman. Hjältarna möter sig själva men denna gång som sina egna litterära avbildningar.Omedvetna om att de också själva är avbildningar.
Nästa station är hos Lewis Carroll,Alices möte med den sovande röde kungen i ”Through the Looking-Glass”.Bröderna Tweedledee och Tweedledum varnar henne mycket allvarligt för att väcka den snarkande kungen som ligger utsträckt i gräset.Som den ordentliga flicka hon är oroar hon sig nämligen för att kungen kanske kan förkyla sig.
’Han drömmer nu’sade Tweedledee:’och kan du tro vad han drömmer om ?’
Alice sade ’Det kan ingen gissa.’
’Jo just om dig’ ropade Tweddledee’ och slog ihop händerna i triumf.’Och ifall han skulle sluta drömma om dig,kan du tänka dig var du skulle hamna då ?”
’Där jag är nu,naturligtvis ’sade Alice.
’Inte du’ genmälde Tweedledee spydigt.’Du skulle inte vara någonstans.Du är bara något slags nånting i hans dröm’
Denna underbara nonsensdialog når en höjdpunkt när Alice påpekar att, om hon är en beståndsdel i den röde Kungens dröm,kan hon knappast heller väcka honom.
Om vi uppfattar de båda delarna av Don Quijote som en enda berättelse, har vi alltså att göra med en berättelse som viks in i sig själv.Vilket skapar osäkerhet om vad som är representationen och vad som är det representerade .I fallet med den sovande röde kungen är det,än mer raffinerat,en dröm som har vikts in i sig själv.
Den tredje klassiker som hängivet ägnar sig åt detta slags konst är Jorge Luis Borges.”Den cirkelformade ruinen” är bara en av de ”Ficciones” där han utforskar detta slags världar som mynnar ut i sig själva.
Vikningar och veckbildningar är i själva verket ytterst intressanta operationer.
Möbiusbandet med dess sällsamma slinga bildar bara en enda yta,Kleins flaska,inte fullt realiserbar i det tredimensionella rummet, har en insida som är dess utsida och vice versa;den påminner med andra ord om vår jordiska existens;vi är inneslutna i ett rum som vi inte kan lämna. Ett argument mot dödsskräck.
Kurt Gödel bevisar att Principia Mathematica och liknande system måste innehålla inom systemet formellt oavgörbara satser.Och sättet att visa detta är med så kallade Gödelnumren.Gödel avbildar matematiken i dess helhet på ett hörn av matematiken genom att ge varje tecken som kan förekomma i en välbildad formel dess unika signum i form av ett tal. Därmed kan hela beviset ges en matematisk behandling.
Denna geniala veckbildning för oss till Douglas Hofstaedters fascinerande böcker, ”Gödel,Escher, Bach” från 1979 och ”I am a strange loop” 2007.Hofstaedter tolkar ett klassiskt filosofiskt problem ,självmedvetandet,som resultatet av en vikning eller en ”strange loop”. Mitt medvetande är en mer eller mindre bristfällig avbildning av världen.Men i denna avbildning finns också avbildningen av mig själv. Eller som den amerikanska flickan säger i ”Den amerikanska flickans söndagar” :
Hur kan vi tala till oss själva
och lyssna som vore det en annan?
Är vi kanske,nogra räknat,mer än en ?
Hur många av oss bor i samma magra kropp ?
Och detta sällsamma som spegeln säger,
att allt det som är jag hör till
en yttre värld som frågar föga efter mig.
Och samtidigt är hela denna yttervärld
det enda som min innervärld består av .
Världen,sinnrikt vikt in i sig själv.
Det är vad spegeln säger.Men kan
då delen vara helheten som i sin tur
är delen ?Någonting är konstigt här.
Jag tror inte alls att vi har fattat världen.
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