Adonis Diaries

Archive for September 13th, 2020

Incomplete: Simplify (Einstein, Godel, Turing, Chaitin…)

One thing we know is that life reinforces the hypothesis that the world is infinitely complex and most of its phenomena will remain incomprehensible, meaning unexplained.

For example, no theory of life evolution was able to predict the next phase in evolution and the route taken to the next phase. The reason we have difficulty discovering how living organism adapt to the environment to survive, in longer term.

We don’t know if laws in biology will exist in the same meaning of laws of physics or natural phenomena.

For example, is the universe simple or complex, finite or infinite?

The mathematician Chaitin answered: “This question will remain without any resolution, simply because we need an external observer outside our system of reference, preferably non-human, to corroborate our theoretical perception.”

(A few of my readers will say: “This smack of philosophy” and they hate philosophy or the rational logic deducted from reduced propositions that cannot rationally be proven)

So many scholars wanted to believe that “God does not play dice” (Einstein) or that chaos is within the predictive laws of God and nature (Leibniz), or that the universe can be explained by simple, restricted set of axioms, non-redundant rules (Stephen Hawking).

Modern mathematical theories and physical observations are demonstrating that most phenomena are basically behaving haphazardly.

For example, quantum physics reveals that hazard is the fundamental principle in the universe of the very tiny particles:  Individual behaviors of small particles in the atomic nucleus are unpredictable.  Thus, there is no way of measuring accurately speed, location, and direction of a particle simultaneously; all that physics can do is assigning probability numbers.

Apparently, hazard plays a role even in mathematics.

For example, many mathematical “true” statesmans cannot be demonstrated, they are logically irreducible and incomprehensible.

Mathematicians know that there exists an infinity of “twin” prime numbers (odd number followed by even number) but this knowledge cannot be proven mathematically.

Thus, many mathematicians would suggest to add these true “propositions” but non demonstrable theories to the basic set of axioms.

Axioms are a set of the bare minimum of “given propositions” that we think we know to be true, but the reason is unable to approach them adequately, using the logical processes.

Einstein said: “What is amazing is that the eternally incomprehensible in nature is comprehensible”; meaning that we always think that we can extend an explanation to a phenomenon without being able to proving its working behaviors.

Einstein wrote that to comprehend means to rationally explain by compressing the basic axioms so that our mind can understand the facts; even if we are never sure how the phenomenon behaves.

For example, Plato said that the universe is comprehensible simply because it looks structured by the beauty of geometric constructs, the regularity of the tonality in string instruments, and steady movement of planets…

Steven Weinberg admits that “If we manage to explain the universal phenomenon of nature it will not be feasible by just simple laws.” (I agree with Weinberg in that statement. Consequently, comprehension will be limited to the few scientists who can handle and visualize complex equations)

Many facts can be comprehended when they are explained by a restricted set of theoretical affirmations:  This is called the Occam Razor theory which says: “The best theory or explanation is the simplest.”

The mathematician Hermann Weyl explained: “We first need to confirm that nature is regulated by simple mathematical laws.  Then, the fundamental relationships become simpler the further we fine-tune the elements, and the better the explication of facts is more exact.”

So what is theory?

Informatics extended another perspective for defining theory: “a theory is a computer program designed to take account of observed facts by computation.  Thus, the program is designed to predict observations.  If we say that we comprehend a phenomenon then, we should be able to program its behavior.  The smaller the program (more elegant) the better the theory is comprehended.”

When we say “I can explain” we mean that “I compressed a complex phenomenon into simple programs that “I can comprehend”, that human mind can comprehend. 

Basically, explaining and comprehending is of an anthropic nature, within the dimension of human mental capabilities.

The father of information theory, John von Neumann wrote: “Theoretical physics mainly categorizes phenomena and tries to find links among the categories; it does not explain phenomena.

In 1931, mathematician Kurt Godel adopted a mental operation consisting of indexing lists of all kinds of assertions.

His formal mathematical method demonstrated that there are true propositions that cannot be demonstrated, called “logically incomplete problems

The significance of Godel’s theory is that it is impossible to account for elemental arithmetic operations (addition or multiplication) by reducing its results from a few basic axioms.  With any given set of logical rules, except for the most simple, there will always be statements that are undecidable, meaning that they cannot be proven or disproven due to the inevitable self-reference nature of any logical systems.

The theorem indicates that there is no grand mathematical system capable of proving or disproving all statements.

An undecidable statement can be thought of as a mathematical form of a statement like “What I just said is a lie”:  The statement makes reference to the language being used to describe it, it cannot be known whether the statement is true or not.

However, an undecidable statement does not need to be explicitly self-reference to be undecidable. The main conclusion of Gödel’s incompleteness theorems is that all logical systems will have statements that cannot be proven or disproven; therefore, all logical systems must be “incomplete.”

The philosophical implications of these theorems are widespread.

The set suggests that in physics, a “theory of everything” may be impossible, as no set of rules can explain every possible event or outcome. It also indicates that logically, “proof” is a weaker concept than “true”.

Such a concept is unsettling for scientists because it means there will always be things that, despite being true, cannot be proven to be true. Since this set of theorems also applies to computers, it also means that our own minds are incomplete and that there are some ideas we can never know, including whether our own minds are consistent (i.e. our reasoning contains no incorrect contradictions).

The second of Gödel’s incompleteness theorems states that no consistent system can prove its own consistency, meaning that no sane mind can prove its own sanity.

Also, since that same law states that any system able to prove its consistency to itself must be inconsistent, any mind that believes it can prove its own sanity is, therefore, insane.

Alan Turing used a deeper twist to Godel’s results.

In 1936, Turing indexed lists of programs designed to compute real numbers from zero to 1 (think probability real numbers).  Turing demonstrated mathematically that no infallible computational procedures (algorithms) exist that permit to decide whether a mathematical theorem is true or false.

In a sense, there can be no algorithm able to know if a computer program will even stop.

Consequently, no computer program can predict that another program will ever stop computing.  All that can be done is allocating a probability number that the program might stop.  Thus, you can play around with all kinds of axioms, but no sets can deduce that a program will end.  Turing proved the existence of non computable numbers.

Note 1: Chaitin considered the set of all possible programs; he played dice for each bit in the program (0 or 1, true or false) and allocated a probability number for each program that it might end.  The probability that a program will end in a finite number of steps is called Omega.  The succession of numbers comprising Omega are haphazard and thus, no simple set of axioms can deduce the exact number.  Thus, while Omega is defined mathematically, the succession of the numbers in Omega has absolutely no structure.  For example we can write algorithm to compute Pi but never for Omega.

Note 2:  Bertrand Russell (1872-1970) tried to rediscover the founding blocks of mathematics “the royal highway to truth”.  He was disappointed and wrote: “Mathematics is infected of non proven postulates and infested with cyclic definitions.  The beauty and the terror of mathematics is that a proof must be found; even if it proves that a theory cannot e be proven”

Note 3:  The French mathematician Poincaré got a prize for supposedly having discovered chaos.  The article was officially published when Poincaré realized that he made a serious error that disproved his original contention.  Poincaré had to pay for all the published articles and for destroying them.  A single copy was saved and found at the Mittag-Leffler Institute in Stockholm.

Beirut was a Movable Fair before the onset of the civil war in 1975

With a strong currency (1$ worth 2 Lebanese pound) and a low cost of living before the onset of civil war in 1975, Beirut was a movable fair for the common people, those living and commuting to Beirut.

Actually, during most of the civil war period, the  LP remained strong due to the massive reserves of hard currencies of the Palestinian Liberation Organization (PLO), from the massive infusion of Gulf Arab States, Saudi Kingdom and Libya…

I recall, while at the university, (1970-75) that I could live for an entire day on barely 2 LP for the cost of Taxis, buses, watching movies, going to theaters, eating and drinking fresh juices and joining daily student demonstrations, marches and sit-in demanding reforms in Lebanon political system.

You may read my memoirs on these wonderful period on https://adonis49.wordpress.com/2019/09/05/movable-fairs-in-beirut-1971-74/

What follows is an article posted by a French woman, a foreigner in 2016, who was overwhelmed by a faked sense of sustainable fair in Beirut. She was taken care of by those 1% “rich” people who kept looting the budget and lived on inherited wealth. Though she was aware of the precarious conditions of this political system and resurgence of violence at any moment.

Beyrouth est une fête

Katherine Pancol. Écrivain

Jean C. El Dahdah shared this link. February 19, 2016

Ça y est! Je reprends goût à la vie! Alors, que vous raconter?

Que le Liban est une bouteille de champagne posée sur un volcan et qu’à Beyrouth, la fête est perpétuelle, frénétique comme une avance que les habitants prennent sur la vie et le prochain conflit…

Les Libanais sont les gens les plus accueillants, les plus affectueux, les plus gais, les plus entreprenants, les plus insouciants, les plus généreux du monde.

La vie, ils l’inventent à chaque minute de peur qu’on ne la leur confisque.

Ils ont cette intuition terrible: la guerre peut surgir n’importe quand, alors vivons pleinement, aimons, dansons, buvons du café noir, du café blanc, fumons de longs narguilés, ouvrons des boutiques, des restaurants, construisons, traînons dans les rues, faisons des carnavals, inventions, célébrons, oublions les feux rouges, l’interdiction de fumer, vivons, vivons, vivons…

Beyrouth est une fête.

Ils ne savent pas d’où le danger va surgir pour leur tomber sur la tête.

Le Liban est une immense boîte à lettres où chaque pays voisin fait passer un message en posant des bombes, en assassinant, en écharpant…

Ce ne sont pas les Libanais qui font la guerre, ce sont les pays autour qui se font la guerre via le Liban. (Le plus souvent Executer par des Libanais)

J’étais allée au Liban une première fois, il y a douze ans. Le pays était alors en pleine reconstruction… après une guerre.

Des gratte-ciel surgissaient au milieu des décombres, des camions déblayaient des tonnes de gravats, les façades étaient criblées de balles, on apercevait, béants au soleil, des bouts de cuisine, de salle de bains, de chambre à coucher, la poussière s’élevait en gros nuages gris qui montaient vers un ciel toujours bleu… et les voitures klaxonnaient, klaxonnaient!

( I returned to Lebanon on Christmas of 2000, and the reconstruction was already over and many people lost their jobs, and the vital Beirut Center was monopolized and changed to accommodate the rich visitors and tourists of the rich “Arabs”. Old Beirut was totally erased, even its memorable specialized and Not expensive Souks)

J’avais déjà été frappée par l’énergie qui vibrait dans l’air. On pouvait la saisir à pleines mains et en faire des éclairs.

Douze ans après (et après bien d’autres guerres!), Beyrouth est toujours debout, les buildings en verre lèchent le ciel, des rues montent et descendent comme à San Francisco délimitant un vieux quartier et des quartiers de luxe, des quartiers d’affaires, des rues du soir, des rues de la nuit, des rues qui grouillent, grouillent.

Tout le monde se mélange à Beyrouth et, semble t-il, dans la bonne humeur…

C’est une impression, je ne suis pas restée assez longtemps, mais je n’ai ressenti aucune tension entre les différentes communautés.

Il y a des femmes en mini-jupes et des femmes voilées, des hommes en djellaba et d’autres en costume cravate et tout le monde vit ensemble.

J’ai couru au Musée de Beyrouth voir les statuettes des guerriers phéniciens…

De longues et minces silhouettes semblables à des Giacometti.

J’ai appris à traverser les rues en étendant le bras, en joignant les mains, en cambrant les reins tel le torero face au noir taureau dans l’arène, en suppliant qu’on ne m’écrase pas!

Il faut ployer, sautiller, frôler la tôle, feinter et passer… pour rejoindre des trottoirs qui font office de garde-meubles, garages, dernier salon où l’on cause.

J’ai compris que les feux rouges sont faits pour être brûlés (Not to abide by the color), sauf les “importants” où l’on consent à s’arrêter, les cigarettes à griller dans tous les restaurants et la vitesse à être constamment dépassée…

J’ai bu du café turc sur la Corniche au bord de la mer. On était en novembre, il faisait 28′  et la mer me chatouillait les pieds.

J’ai marché dans les rues avec Rachid El Daïf, un auteur libanais qui a écrit un très bon roman paru chez Actes Sud, “Qu’elle aille au diable, Meryl Streep!”, et nous sommes allés nous poser dans les jardins du café Al Rawda…

J’ai parlé avec Tania, éditrice, qui se bat pour sauver les vieilles maisons de Beyrouth de la convoitise des spéculateurs immobiliers, avec Katya qui peint, j’ai déjeuné au People avec Dédy, un ami tombé dans les livres quand il était petit, dîné avec Émile, librairie chez Virgin, j’ai été invitée partout, partout et chaque fois, reçue les bras grands ouverts et la gourmandise aux lèvres.

Les Libanais sont curieux, raffinés, cosmopolites.

Ils commencent une phrase en arabe, la truffent de mots anglais et français, parlent avec les cheveux, les mains, les yeux

Le soir de mon arrivée, j’ai dîné à la même table avec des Libanais de toutes familles: des chrétiens, des musulmans, des chiites, des sunnites, des maronites, des druzes, des catholiques, des orthodoxes, des riches, des pauvres, des bons vivants, des austères, des grands, des petits, et ils parlaient tous sans s’écharper.

De la Palestine et d’Israël, des USA et de l’Arabie Saoudite et pas une minute, ils n’en sont venus aux mains! J’imaginais le même dîner en France…

Je suis allée avec Dédy à Saïda visiter un vieux palais, le palais Debbané, niché en plein souk, une ancienne maison familiale où une pièce entière est dévolue à de gigantesques volières disposées de chaque coté et j’ai imaginé des concerts d’oiseaux en stéréo!

Nous avons visité le musée du savon Audi, toujours dans le souk, une résidence magnifique où l’on déroule pour vous toute l’histoire de la fabrication du savon… et un caravansérail, construit par des Français au moment des Croisades.

Sur la terrasse d’un restaurant face au Château des Croisés qui s’avance dans la mer, j’ai pensé à Joséphine et au XII ème siècle! Elle me racontait des histoires de Croisés qui ont fait souche, de Croisés qui ont péri, de Croisés qui ont pillé, de Croisés qui ont construit et je l’écoutais, ébahie.

Toutes les notes que j’avais prises pour les recherches de Joséphine revenaient et se mélangeaient aux images de Saïda et de la forteresse…

Au retour, nous nous sommes arrêtés dans une orangeraie et une femme a pressé des oranges, des pamplemousses, des mandarines et des citrons rien que pour nous. Il y avait des jouets d’enfants répandus sous une tonnelle, du linge qui séchait, des figues ventrues, un vieux jardinier, des arbres ployaient sous les fruits, des rigoles irriguaient le pied des arbres… Le temps s’est arrêté.

On se parlait avec les mains, avec les yeux et c’était délicieux…

Vous avez compris, j’ai aimé le Liban. Beaucoup, beaucoup.

C’est un pays de lumière où la vie pétille et chante… une belle leçon de courage et de bonne humeur!

Note: You were a visitor Katheirne and from a western country to boot it. Don’t be fooled by the sincerity and welcoming attitudes. In any case, you didn’t stay long enough to discover the precarity of most Lebanese. The Lebanese have changed for the worst in all aspects, but Not in their sectarian identity and zeal for their feudal/sectarian leaders.


adonis49

adonis49

adonis49

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