All posts by georgsaliba

www.choiceofneurosis.wordpress.com

Rousseau on Inequality

You’ve probably read this many times before , and so has humanity in the last centuries, and yet, its eloquence intact, it resonates today more stridently than ever. Read well… :

(Being originally Francophone, I couldn’t help but include the original French text, followed by an English translation).

“Le premier qui, ayant enclos un terrain, s’avisa de dire: Ceci est à moi, et trouva des gens assez simples pour le croire, fut le vrai fondateur de la société civile. Que de crimes, de guerres, de meurtres, que de misères et d’horreurs n’eût point épargnés au genre humain celui qui, arrachant les pieux ou comblant le fossé, eût crié à ses semblables: Gardez-vous d’écouter cet imposteur; vous êtes perdus, si vous oubliez que les fruits sont à tous, et que la terre n’est à personne.”

“The first man who, having enclosed a piece of ground, bethought himself of saying This is mine, and found people simple enough to believe him, was the real founder of civil society. From how many crimes, wars, and murders, from how many horrors and misfortunes might not any one have saved mankind, by pulling up the stakes, or filling up the ditch, and crying to his fellows: Beware of listening to this imposter; you are undone if you once forget that the fruits of the earth belong to us all, and the earth itself to nobody.”

Jean-Jacques Rousseau, Discours sur l’origine et les fondements de l’Inégalité

Jean-Jacques-Rousseau1

Gödel’s Proof

Gödel showed (i) how to construct an arithmetical formula G that represents the meta-mathematical statement: ‘The formula G is not demonstrable’. This formula G thus ostensibly says of itself that it is not demonstrable. Up to a point, G is constructed analogously to the Richard Paradox. In that Paradox, the expression ‘Richardian’ is associated with a certain number n, and the sentence ‘n is Richardian’ is constructed. In Gödel’s argument, the formula G is also associated with a certain number h, and is so constructed that it corresponds to the statement: ‘The formula with the associated number h is not demonstrable’. But (ii) Gödel also showed that G is demonstrable if, and only if, its formal negation ~G is demonstrable. This step in the argument is again analogous to a step in the Richard Paradox, in which it is proved that n is Richardian if, and only if, n is not Richardian. However, if a formula and its own negation are both formally demonstrable, the arithmetical calculus is not consistent. Accordingly, if the calculus is consistent, neither G nor ~ G is formally derivable from the axioms of arithmetic. Therefore, if arithmetic is consistent, G is a formally undecidable formula.  Gödel then proved (iii) that, though G is not formally demonstrable, it nevertheless is a true arithmetical formula. It is true in the sense that it asserts that every integer possesses a certain arithmetical property, which can be exactly defined and is exhibited by whatever integer is examined, (iv) Since G is both true and formally undecidable, the axioms of arithmetic are incomplete. In other words, we cannot deduce all arithmetical truths from the axioms. Moreover, Gödel established that arithmetic is essentially incomplete: even if additional axioms were assumed so that the true formula G could be formally derived from the augmented set, another true but formally undecidable formula could be constructed, (v) Next, Gödel described how to construct an arithmetical formula A that represents the meta-mathematical statement: ‘Arithmetic is consistent’; and he proved that the formula ‘A ⊃ G’ is formally demonstrable. Finally, he showed that the formula A is not demonstrable. From this it follows that the consistency of arithmetic cannot be established by an argument that can be represented in the formal arithmetical calculus.

(From Nagel and Newman‘s “Gödel’s Proof”

The Probable Origins of “Amy Farrah Fowler”

All of The Big Bang Theory fans know that some characters from the show borrow their names from actual people. For example “Leonard Hofstadter” is derived from Sheldon Leonard (actor/producer) and Robert Hofstadter (Physicist and Nobel Prize Laureate) while “Sheldon Cooper” is also derived from Sheldon Leonard and another Nobel Prize Laureate in Physics: Leon Cooper. The names are thus combinations of “Acting” and “Science”. But how about “Amy Farrah Fowler”? Does it have an origin in reality, or is it just another random quirky name?

The “Brain-Eating Amoeba”

Recently, while doing a little research about epidemics and diseases, I stumbled upon an article about an AMOEBA called N. FOWLERI (It was named after Physician M.Fowler)… AMY Farrah FOWLER…  Am I the only one who hears the phonetic similarity? In addition, this amoeba is nicknamed “the brain-eating amoeba” (for obvious reasons), and we all know how enticing a disease ridden brain is for good old Amy. Well, that covers the “Science” part of the equation, how about the “Acting”? To be honest, I’m not sure, but Farrah Fawcett seems like a good candidate for the part. Why you ask? Well, the fact that Amy is (physically speaking) Fawcett’s diametric opposite adds to her comicality and to the many contrasts of her personality.

In conclusion, all of this is nothing but hypothetical since none of the show’s producers, directors, writers etc. has ever mentioned any origin to Amy’s name. But still, there’s no harm in musing about it!

Tonic or Cereal?

“Achilles : Oh, I couldn’t tell. Well, now I REALLY want to            find that bottle of tonic. For some reason, my lips              are burning. And nothing would taste better than            a drink of popping-tonic.
Tortoise : That stuff is renowned for its thirst quenching            powers. Why in some places people very nearly go         crazy over it. At the turn of the century in Vienna,              the Schönberg food factory stopped making tonic,          and started making cereal instead. You can’t                   imagine the uproar that caused.”

Douglas HOFSTADTER,
in “Gödel, Escher, Bach: an Eternal Golden Braid”
M.C.Escher’s Convex and Concave (1955 Lithograph)